chapter08

Introduction to Conditional Logic

Conditional logic. The phrase itself has been known to induce the sweats for many an LSAT test-taker. Yes, knowing and understanding conditional logic is important for your success on the LSAT, but it doesn't have to cause you undue anxiety. We got you started with the basics in Chapter 2, but we're going to start over from the beginning here to be sure that your foundation is solid. Then we'll take you through the tough stuff. By the end of this chapter, you'll be able to use your conditional logic skills to fight off some of the toughest logical reasoning questions out there. Let's get started.

Back to the Basics

(NOTE: If you truly understand simple conditional statements and their contrapositives, you may skip to the Application section. Don't make this decision lightly, though. The review can't hurt.)

As promised, we're going to start at the beginning. Remember this example?

When Jasmine wakes up early in the morning, she is not productive at work that day. Jasmine woke up early in the morning on Wednesday.

If the above statements are true, which one of the following must also be true?

(A) If Jasmine was unproductive at work on any particular day, then she must have woken up early on that day.

(B) Jasmine was not productive at work on Wednesday.

This abbreviated Logical Reasoning question contains a conditional relationship. If condition X (waking up early) is met, then Y (unproductive at work) is guaranteed. Thus, if Jasmine woke up early on Wednesday, then we can infer that she was not productive at work on Wednesday. Answer (B) is correct.

Doesn't (A) seem correct too? In fact, it is NOT necessarily correct. Let's explore the ins and outs of conditional logic in order to fully understand why not.

What Is a Conditional Statement?

A conditional statement expresses a guaranteed outcome when a specific condition is met. The most basic type of conditional statement uses “If…then” phrasing:

IF Jeremy eats a big lunch, THEN he won't be hungry for dinner.

IF John lives in San Francisco, THEN John lives in California.

IF Sue attends the concert, THEN her husband is at home babysitting the children.

IF Hiromi wins the election, THEN she had the most organized campaign.

It's important to note that conditional statements are sometimes disguised. As an example, consider this statement again:

When Jasmine wakes up early in the morning, she is not productive at work that day.

This statement is not written in If/Then form, but it indeed is a conditional statement. Again, when condition X (waking up early) is satisfied, then Y (unproductive at work) is guaranteed. A simple and effective way to think about all conditional statements is that they express guarantees. We can phrase this in If/Then form:

IF Jasmine wakes up early in the morning, THEN (it is guaranteed) she is not productive at work that day.

Sufficient vs. Necessary Condition

The “If” part of the conditional statement is called the sufficient condition because it is sufficient, or enough by itself, to guarantee the truth of the “Then” part of the statement. The “Then” part of the statement is called the necessary condition because, when the sufficient condition is true, it is required, or necessary, that the “Then” portion be true as well. To summarize:

Sufficient Condition: The “If” part of the statement. When satisfied, it is sufficient on its own to guarantee the outcome.

Necessary Condition: The “Then” part of the statement. It is guaranteed to be true when the sufficient condition is satisfied.

Note that while the sufficient condition is sufficient to guarantee the truth of the necessary condition, or outcome, it is not necessarily required to arrive at this outcome. This is a critical difference. Let's take a look at another very simple example to illustrate.

IF you buy me a gift, THEN I will be happy.

Buying me a gift guarantees my happiness, but is it the only thing that would make me happy? Not necessarily. Here are some other possibilities:

So, what can we conclude? Two things for now:

1. You giving me a gift is sufficient to guarantee that I will be happy (note the arrow signifying the guaranteed outcome).

2. You giving me a gift is not required to guarantee that I will be happy. If I am happy, this does NOT guarantee that you have given me a gift (maybe I'm happy for a different reason—maybe I got a raise, or maybe the weather is nice). In other words, the relationship doesn't necessarily work the other way around!

Conditional Inferences

Valid vs. Invalid

Before we get back to our “happiness” example, let's consider the following:

IF Sally lives in Boston, THEN Sally lives in Massachusetts.

Based on real life understanding of U.S. geography, we know this statement to be true. Now consider the validity of the following inferences that could be made given the statement above:

1. Is the negative true? If Sally does not live in Boston, then is it guaranteed that Sally does not live in Massachusetts?

2. Is the reverse true? If Sally lives in Massachusetts, then is it guaranteed that Sally lives in Boston?

3. Is the negative AND reverse true? If Sally does not live in Massachusetts, then is it guaranteed that Sally does not live in Boston?

This is a simpler case because you already know that Boston is not the only city or town in Massachusetts. You can probably see already that the first and second inferences are NOT valid. Even so, let's use our picture to illustrate (Worcester, Newton, and Cambridge are other cities in Massachusetts):

1. If Sally does not live in Boston, then is it guaranteed that Sally does not live in Massachusetts? No. After all, Sally could live in Newton, which would still put her in MA.

2. If Sally lives in Massachusetts, then is it guaranteed that Sally lives in Boston? This isn't necessarily true either. There are many places Sally could live, including Cambridge, Worcester, and Newton, that are in Massachusetts but outside of Boston. Yes, Boston guarantees Massachusetts, but Massachusetts does not guarantee Boston!

3. If Sally does not live in Massachusetts, then is it guaranteed that Sally does not live in Boston? Yes! This, of course, MUST be true. If Sally does not live in the state of Massachusetts, it is not possible for her to live in Boston. This is the only inference of the bunch that is valid.

Let's now apply the same logic to the “happiness” example, which is a bit tougher:

IF you give me a gift, THEN I will be happy.

Now consider the following related inferences that might be made given the statement above:

1. The NEGATION: If you do not give me a gift, then I will not be happy.

2. The REVERSAL: If I am happy, then you have given me a gift.

3. The REVERSAL and NEGATION: If I am not happy, then you have not given me a gift.

Which of these inferences, if any, are valid? To evaluate our potential inferences, let's consider our picture again, remembering that there may be other sufficient conditions that would guarantee “my happiness.”

1. If you do not give me a gift, then I will not be happy. This, of course, is not necessarily true. Remember, while giving me a gift is sufficient to make me happy, it is not required. Maybe you haven't given me a gift, but perhaps I am happy because I got a raise at work today. Thus, this is an invalid inference.

2. If I am happy, then you have given me a gift. Remember, there could be other reasons why I am happy. This is an invalid inference.

3. If I am not happy, then you have not given me a gift. This MUST be true. Gift automatically guarantees happiness. So, if I am not happy, you could not have possibly given me a gift. This is the only valid inference of the bunch.

By now you may be noticing that the only correct inference, regardless of the original conditional statement, is one that reverses and negates the original.

We can reduce this complex train of thought to a reliable rule. To do so, let's start by organizing our thinking through the use of symbols. Let's use a G to symbolize “You buy me a gift” and an H to symbolize “I will be happy.” The arrow indicates the “If…then” relationship:

You can see by looking at the symbols that the first inference simply negates the components of the original given statement. The second inference simply reverses the original components. The third inference both reverses and negates the components of the original statement. Thus, the only valid inference is one that reverses and negates the form of the original given statement. This is called the contrapositive.

Contrapositive: The valid inference derived by reversing and negating the components of the given conditional statement.

Let's generalize:

So, what have we learned? We've learned that any time we have a conditional statement, we know with certainty that the contrapositive statement is also true.

Revisiting Jasmine

Here's our example from the start of the chapter. Take a second now to think about why (A) is NOT a correct answer:

When Jasmine wakes up early in the morning she is not productive at work that day. Jasmine woke up early in the morning on Wednesday.

If the above statements are true, which one of the following must also be true?

(A) If Jasmine was unproductive at work on any particular day, then she must have woken up early on that day.

(B) Jasmine was not productive at work on Wednesday.

If you said that answer (A) illegally reverses the logic, you would be correct! Let's diagram the situation:

Answer choice (A) is the equivalent of inference #2 in the table above. Bad inference!

Let's practice what we've learned so far.

DRILL IT: Conditional Statements and Contrapostives

Diagram each of the conditional statements below, then diagram the contrapositive relationship by reversing and negating the components of the original. Finally, use the contrapositive diagram to write a statement that expresses the valid inference made. Be sure to check your responses against the solutions after each one.

Example: GIVEN: If X is not selected, then Y is selected.

GIVEN DIAGRAM: –X Y

CONTRAPOSITIVE DIAGRAM: –Y X

VALID INFERENCE: If Y is not selected, then X is selected.

1. GIVEN: If Sid is on the committee, then Jana is on the committee.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

2. GIVEN: If Raul is invited to the party, then Shaina is not invited to the party.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

3. GIVEN: If Brooks is not on the bus, then Traiger is not on the bus.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

4. GIVEN: If the tiger is not in the cage, then the lion is in the cage.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

5. GIVEN: I will not go jogging if it is raining outside.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

6. GIVEN: Yohei plays guitar if Juan plays drums.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

7. GIVEN: If T is not chosen for the team, then N is not chosen for the team.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

8. GIVEN: G is not selected for the club if F is selected for the club.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

9. GIVEN: If Beethoven is played, then Mozart is also played.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

10. GIVEN: Dmitry might play volleyball or squash, but he definitely can't play both.

GIVEN DIAGRAM:

CONTRAPOSITIVE DIAGRAM:

VALID INFERENCE:

SOLUTIONS: Conditional Statements and Contrapositives

1. GIVEN: If Sid is on the committee, then Jana is on the committee.

GIVEN DIAGRAM: S J

CONTRAPOSITIVE DIAGRAM: –J –S

VALID INFERENCE: If Jana is not on the committee, then Sid is not on the committee.

2. GIVEN: If Raul is invited to the party, then Shaina is not invited to the party.

GIVEN DIAGRAM: R S

CONTRAPOSITIVE DIAGRAM: S –R

VALID INFERENCE: If Shaina is invited to the party, then Raul is not invited to the party.

3. GIVEN: If Brooks is not on the bus, then Traiger is not on the bus.

GIVEN DIAGRAM: –B –T

CONTRAPOSITIVE DIAGRAM: T B

VALID INFERENCE: If Traiger is on the bus, then Brooks is on the bus.

4. GIVEN: If the tiger is not in the cage, then the lion is in the cage.

GIVEN DIAGRAM: –T L

CONTRAPOSITIVE DIAGRAM: –L T

VALID INFERENCE: If the lion is not in the cage, then the tiger is in the cage.

5. GIVEN: *I will not go jogging if it is raining outside. = If it is raining outside, then I will not go jogging.

GIVEN DIAGRAM: R images –J

CONTRAPOSITIVE DIAGRAM: J images –R

VALID INFERENCE: If I go jogging, then it is not raining outside.

*Be careful with this one! Notice that the original given statement has a unique structure.

6. GIVEN: Yohei plays guitar if Juan plays drums. = If Juan plays drums, then Yohei plays guitar.

GIVEN DIAGRAM: JD images YG

CONTRAPOSITIVE DIAGRAM: –YG images –JD

VALID INFERENCE: If Yohei does not play guitar, then Juan does not play drums.

7. GIVEN: If T is not chosen for the team, then N is not chosen for the team.

GIVEN DIAGRAM: –T images –N

CONTRAPOSITIVE DIAGRAM: N images T

VALID INFERENCE: If N is chosen for the team, then T is chosen for the team.

8. GIVEN: G is not selected for the club if F is selected for the club. = If F is selected for the club, then G is not selected.

GIVEN DIAGRAM: F images –G

CONTRAPOSITIVE DIAGRAM: G images –F

VALID INFERENCE: If G is selected for the club, then F is not selected for the club.

9. GIVEN: If Beethoven is played, then Mozart is also played.

GIVEN DIAGRAM: B images M

CONTRAPOSITIVE DIAGRAM: –M images –B

VALID INFERENCE: If Mozart is not played, then Beethoven is not played.

10. GIVEN: Dmitry might play volleyball or squash, but he definitely can't play both.

GIVEN DIAGRAM:

–S or S images

–V

This is a tricky one! The conditional logic is hidden a bit here.

CONTRAPOSITIVE DIAGRAM: S images –V or V images –S

VALID INFERENCE: If Dmitry plays volleyball, then he does not play squash. And, if Dmitry plays squash, then he does not play volleyball.

Applying Conditional Logic 1: The Basics

Now that you've got the basics under your belt, let's see how an understanding of standard conditional statements and contrapositives can help you on an actual LSAT problem. Give yourself 1:20 to answer the following question.

PT36, S1, Q26

In the paintings by seventeenth-century Dutch artist Vermeer, we find several recurrent items: a satin jacket, a certain Turkish carpet, and wooden chairs with lion's-head finials. These reappearing objects might seem to evince a dearth of props. Yet we know that many of the props Vermeer used were expensive. Thus, while we might speculate about exactly why Vermeer worked with a small number of familiar objects, it was clearly not for lack of props that the recurrent items were used.

The conclusion follows logically if which one of the following is assumed?

(A) Vermeer often borrowed the expensive props he represented in his paintings.

(B) The props that recur in Vermeer's paintings were always available to him.

(D) The several recurrent items that appeared in Vermeer's paintings had special sentimental importance for him.

(E) If a dearth of props accounted for the recurrent objects in Vermeer's paintings, we would not see expensive props in any of them.

By now, you should be comfortable recognizing this as an Assumption Family question, and you should be familiar with the optimal approach for attacking such questions. Let's run through it.

DECISION #1: What is my task?

This question is asking us to select an assumption that would allow the conclusion to follow logically. In other words, we need a sufficient assumption.

(NOTE: We've now used the word sufficient in two different contexts: sufficient assumption and sufficient condition. Just as a reminder, a sufficient assumption is an assumption that is enough on its own to get to the conclusion. As we've just learned, a sufficient condition is a condition that is enough on its own to guarantee an outcome. While the term sufficient is used in two different contexts, the implication is the same in both: one thing is sufficient, or enough, on its own to lead to, guarantee, or require something else.)

DECISION #2: What is the author's conclusion?

DECISION #3: How is that conclusion supported?

Let's read the argument again with the above questions in mind:

In the paintings by seventeenth-century Dutch artist Vermeer, we find several recurrent items: a satin jacket, a certain Turkish carpet, and wooden chairs with lion's-head finials.

Background information so far.

These reappearing objects might seem to evince a dearth of props.

“…might seem…” Sounds like the author is about to counter this viewpoint.

Yet we know that many of the props Vermeer used were expensive.

Yes. The word “yet” is a pivot word. So, some might say that Vermeer used the same props over and over again because he was lacking in props, but the author is countering this viewpoint.

Thus, while we might speculate about exactly why Vermeer worked with a small number of familiar objects, it was clearly not for lack of props that the recurrent items were used.

Okay, this is the conclusion. Vermeer was not lacking in props. He had plenty (and we know this because his props were expensive). So the argument core is:

Vermeer used expensive props.

Vermeer was not lacking in props.

It's important that we really understand the logic behind this argument. Think about it. If your friend drove the same Porsche around for 10 years, would you conclude that he hadn't bought a new car because he was lacking in means? Probably not. He drives an expensive Porsche! You would likely conclude that he has plenty of money to get a different car if he wanted to. He's sticking with his Porsche, but it's probably not because he's lacking the means to get something else.

The same sort of logic is used here. Because Vermeer's props were expensive, the author concludes that Vermeer could have had access to other props if he wished. The question is, does this make a valid argument?

DECISION #4: What is the gap?

The author assumes that because the props were expensive he must have had access to many more props. So, in attempting to explain why Vermeer would use the same props repeatedly, the author rules out the possibility that he didn't have access to other props. This doesn't necessarily need to be the case. Maybe the expensive props were gifted to Vermeer and those were the only ones he had access to. Maybe he didn't have the money to buy new props because he spent all his money on those few expensive ones. Maybe he'd borrowed those props.

Okay, at this point we have a sense for what might come up in the answer choices.

DECISION #5: Which answer choices are clearly wrong?

The easiest eliminations will be answers that aren't related to the argument core. Here's our core again:

Vermeer used expensive props.

Vermeer was not lacking in props.

(A) Vermeer often borrowed the expensive props he represented in his paintings.

Ooh, this is attractive! Be careful though. This actually weakens the argument. If he had borrowed the expensive props (likely because he couldn't purchase them on his own), it wouldn't make sense to conclude that he had the means to access many props. It would actually suggest that he WAS lacking in props. Eliminate it.

(B) The props that recur in Vermeer's paintings were always available to him.

This seems like it might work. It seems related to the conclusion. If they were always available to him, then he wasn't lacking in props. Keep it for now.

Again, this actually weakens the argument. If he had borrowed the expensive props, there would be reason to believe that he WAS lacking in props. Remember, correct assumption answers ought to strengthen the argument, not weaken it. Eliminate this answer.

(D) The several recurrent items that appeared in Vermeer's paintings had special sentimental importance for him.

This is attractive. Maybe he uses these props repeatedly because he's emotionally attached to them and NOT because he's lacking in props. This seems to help. Keep it for now.

(E) If a dearth of props accounted for the recurrent objects in Vermeer's paintings, we would not see expensive props in any of them.

This is the only answer choice that mentions both the expensive props and the lack of props (“dearth of props”). There seems to be a connection made between the two in this answer choice. Keep it.

DECISION #6: What is the best available answer?

We are down to three answer choices. When making a final decision, it's critical that we revisit the core. The correct answer will be the one that most clearly addresses the relationship between the premise and the conclusion:

Vermeer used expensive props.

Vermeer was not lacking in props.

(B) The props that recur in Vermeer's paintings were always available to him.

On second glance, (B) seems unrelated. The conclusion that Vermeer was not lacking in props refers to other props aside from the ones he used regularly. The fact that his recurring props were always available to him doesn't make it any more likely that he was not lacking in other props. Furthermore, what does this have to do with the cost of the props?

(D) The several recurrent items that appeared in Vermeer's paintings had special sentimental importance for him.

This might explain why he used those props over and over again, but it doesn't give us any more reason to argue that since the props he used were pricey he was not lacking in props. Maybe he used the same props over and over because he was sentimental about them, but maybe he was also lacking in other props! This answer is not enough to ensure that the conclusion follows logically from the premise.

Down to answer (E). Let's look at the core one more time:

Vermeer used expensive props.

Vermeer was not lacking in props.

We can think of this argument as having the structure “A. Therefore, B.” The simplest sufficient assumption to any argument of this form is: “If A, then B.” For the above argument, that would look like this: “If Vermeer used expensive props, then Vermeer was not lacking in props.”

Let's imagine what this would look like inserted this into our argument:

Vermeer used expensive props. (If Vermeer used expensive props, then Vermeer was not lacking in props.) Thus, Vermeer was not lacking in props.

Notice the simple conditional statement would make the argument valid by connecting premise to conclusion.

Let's take a look at (E) one more time:

(E) If a dearth of props accounted for the recurrent objects in Vermeer's paintings, we would not see expensive props in any of them.

Let's try to think about this answer choice in simple “If/Then” terms:

“If a lack of props did account for recurring objects, then we would not see expensive props.”

Is this answer what we were looking for? Not exactly. But it seems related. Let's compare the conditional in this answer choice with the conditional we originally determined would be sufficient.

Sufficient Conditional: If Vermeer used expensive props, then Vermeer was not lacking in props. EP –LP.

Conditional in (E): If a lack of props did account for recurring objects, then we would not see expensive props. LP –EP.

Do you notice the relationship between the two? This answer is the contrapositive of what we need! If we reverse and negate it, we can infer the assumption that bridges the gap between the premise and conclusion. EP –LP.

Perhaps (E) seemed somewhat relevant but a bit confusing, on your first read. When examined through the conditional logic lens, (E) is clearly correct.

The above question has a logical structure that is worth noting, since many Sufficient Assumption questions play on this form. Here it is again:

Original Argument: A. Therefore, B.
Sufficient Assumption: If A, then B. Make an assumption explicit.

The correct answer could be “If A, then B” or its contrapositive,“If not B, then not A.”

Compound Conditional Statements

Compound conditional statements are statements that have a two-part sufficient condition (a two-part trigger such as “if X and Y, then…”) and/or a two-part necessary condition (a two part outcome such as “…then Y or Z”). The following example has a two-part outcome:

If M is selected, then both G and H must be selected.

What do we know? If M is selected, then G must be selected. Also, if M is selected, then H must be selected. We can deal with this by splitting the statement into two separate conditionals:

If M is selected, then G is selected. (M G)
If M is selected, then H is selected. (M H)

While this is the most common type of compound statement that you'll see, it's not the only type. Let's take a moment to define the four types of compound statements that are fair game on the LSAT, starting with the type discussed above.

1. AND in the outcome: If M is selected, then both G and H must be selected.

In this case, M, the sufficient condition, is enough to trigger both G and H. In other words, M alone is enough to trigger G, and M alone is enough to trigger H. Thus, we can split the compound statement into two simple statements as we've already learned to do:

If M is selected, then G is selected. (M G)
If M is selected, then H is selected. (M H)

Of course, from these two simple statements we can derive two contrapositives:

If G is not selected, then M is not selected. (–G –M)
If H is not selected, then M is not selected. (–H –M)

It's important to note that this type of compound statement won't always have the word “and” explicitly written in the outcome. For example:

If M is selected, then G is selected but H is not.

This is the same type of compound statement in disguise! Selecting M triggers two outcomes: G is selected AND H is not selected. We can split this up as follows:

M G
M –H

2. OR in the trigger: If M or G is selected, then H must be selected.

In this case, M on its own is enough to trigger H. We can say the same for G. Either one is enough to trigger the outcome, H. Thus, we can split this compound statement into two simple statements:

If M is selected, then H is selected. (M H)
If G is selected, then H is selected. (G H)

Again, we can generate contrapositives:

If H is not selected, then M is not selected. (–H –M)
If H is not selected, then G is not selected. (–H –G)

3. AND in the trigger: If M and G are selected, then H is selected.

Here, both M and G together are enough to trigger H, but we're not sure if either one alone is enough. Thus, we CANNOT split this statement into two parts. We must keep it together:

M + G H

Oh boy. So how on earth can we take the contrapositive of a statement like this? Well, let's think about it. M and G together give us H. If we don't have H, then we couldn't have had M and G together. In other words, if we don't have H, either M is missing or G is missing (or both). –H means –M or –G. To find the contrapositive of a statement like this, reverse and negate the elements and SWAP “AND” for “OR”:

–H –M or –G

Note: It's important to know that “–M or –G” leaves open the possibility that neither is selected. It's not necessarily one or the other. For example, if you're told “Either Tamara or Igor will be invited,” we know for certain that at least one of them must be invited. It's a small example of the difference between our everyday language and the legalistic language used by the LSAT—and law students!

4. OR in the outcome: If M is selected, then G or H is selected.

Notice that M is enough to trigger G or H, but not necessarily both. Thus, we CANNOT split this statement into two parts. We must keep it together:

M G or H

Again, to find the contrapositive, reverse, negate, and SWAP “OR” for “AND” or vice versa:

–G + –H –M

The last three compound statement types are quite rare on the LSAT, but you need to be prepared to deal with them if they do show up. Let's summarize the four types:

Time to practice.

DRILL IT: Compound Conditional Statements

Convert each of the statements into conditional diagrams, and then derive contrapositive inferences. Be sure to check your responses against the solutions after each exercise.

Example: If X is selected, then both Y and Z are selected.

	Conversions:	Contrapositives:
	X Y	–Y –X
	X Z	–Z –X

1. If H is selected, then J is selected but G is not.

2. If K is selected, then neither M nor N is selected.

3. If both P and Q are on the team, then R is on the team.

4. If Paulson is selected, then Oster is selected but Vicenza is not.

5. If both X and Y are chosen, Z is chosen.

6. If the car is red or green, then it is a used car.

7. A good parent is both empathetic and sympathetic.

8. A country is economically healthy if it has both a skilled labor force and a competent government.

9. If one lives with both peace and love, then happiness is attainable.

SOLUTIONS: Compound Conditional Statements

1. If H is selected, then J is selected but G is not.

	Conversions:	Contrapositives:
	H J	–J –H
	H –G	G –H

2. If K is selected, then neither M nor N is selected.

Be careful! “Neither/nor” is NOT the same as “or.” “Neither/nor” is the same as neither one! We can translate “neither M nor N” to “not M and not N.”

	Conversions:	Contrapositives:
	K –M	M –K
	K –N	N –K

3. If both P and Q are on the team, then R is on the team.

	Conversions:	Contrapositives:
	P + Q R	–R –P or –Q

4. If Paulson is selected, then Oster is selected but Vicenza is not.

	Conversions:	Contrapositives:
	P O	–O –P
	P –V	V –P

5. If both X and Y are chosen, Z is chosen.

	Conversions:	Contrapositives:
	X + Y Z	–Z –X or –Y

6. If the car is red or green, then it is a used car.

	Conversions:	Contrapositives:
	R U	–U –R
	G U	–U –G

7. A good parent is both empathetic and sympathetic.

	Conversions:	Contrapositives:
	GP E	–E –GP
	GP S	–S –GP

8. A country is economically healthy if it has both a skilled labor force and a competent government.

	Conversions:	Contrapositives:
	SLF + CG EH	–EH –SLF or –CG

9. If one lives with both peace and love, then happiness is attainable.

	Conversions:	Contrapositives:
	P + L HA	–HA –P or –L

Applying Conditional Logic 2: Compound Conditional Statements

Let's apply these skills to a real LSAT question. Take 1:20, and then we'll discuss.

PT22, S2, Q18

To classify a work of art as truly great, it is necessary that the work have both originality and far reaching influence upon the artistic community.

The principle above, if valid, most strongly supports which one of the following arguments?

(A) By breaking down traditional schemes of representation, Picasso redefined painting. It is this extreme originality that warrants his work being considered truly great.

(B) Some of the most original art being produced today is found in isolated communities, but because of this isolation these works have only minor influence, and hence cannot be considered truly great.

(C) Certain examples of the drumming practiced in parts of Africa's west coast employ a musical vocabulary that resists representation in Western notational schemes. This tremendous originality coupled with the profound impact these pieces are having on musicians everywhere, is enough to consider these works to be truly great.

(D) The piece of art in the lobby is clearly not classified as truly great, so it follows that it fails to be original.

(E) Since Bach's music is truly great, it not only has both originality and a major influence on musicians, it has broad popular appeal as well.

This question is a Principle question that requires us to find an answer that illustrates the given principle. This is a Principle Example question. We'll study these in the next chapter. Note that this is NOT the same as a Principle Support question (the kind we studied in the last chapter).

Did you recognize the given principle as a conditional statement? It's not written in traditional “If/Then” form, but it is a conditional statement nonetheless. A bit later, we'll discuss disguised conditionals in greater detail. For now, just know that the word “necessary” is a conditional trigger. It makes sense, right? Every conditional statement has a necessary component, or outcome. So, if one thing makes something else necessary, you've got a conditional situation on your hands. In this case, to be an example of truly great art (TGA), two things are necessary: (1) originality (O), and (2) far reaching influence on the artistic community (FRI). In other words:

If TGA, then both O and FRI.

TGA O + FRI

Look! A compound conditional statement! Now, we're looking for an answer choice that conforms to this principle, or conditional statement. What would a correct answer look like? Well, a correct answer might give us a TGA, and then describe how it is both O and FRI. Or, and this is the more likely scenario, a correct answer might play off of the contrapositive of this principle:

–O or –FRI –TGA

Since either –O, or –FRI, by itself, guarantees –TGA, we can split this conditional statement into two parts:

–O –TGA
–FRI –TGA

Maybe the answer will describe how a particular art is either not O, or not FRI, and then conclude that the art is not truly great. Let's look at the choices, but before we do, we'll revisit the principle one last time:

TGA O + FRI
–O –TGA
–FRI –TGA

Any answer choice that conforms to any one of the three statements above will be a correct answer.

(A) By breaking down traditional schemes of representation, Picasso redefined painting. It is this extreme originality that warrants his work being considered truly great.

This says the work is O (“redefined painting”), so it must be TGA (O TGA). Does this fit the principle? No, it does not. Eliminate it.

This says the work is O, but also that it is –FRI (not far-reaching). Because it is –FRI, it is –TGA. Does this match the principle? Indeed it does: –FRI –TGA.

This is very tempting. The work is both O and has FRI. Thus, the answer states, it must be TGA: O + FRI TGA

Be careful. This is the exact reverse of the original principle! We can't simply reverse the terms. This is incorrect. While great art must be original and have a far reaching influence, a piece of art could have those characteristics and not be great.

(D) The piece of art in the lobby is clearly not classified as truly great, so it follows that it fails to be original.

–TGA –O. This is a reversal of what we've got as well. Eliminate it.

(E) Since Bach's music is truly great, it not only has both originality and a major influence on musicians, it has broad popular appeal as well.

TGA O + FRI + BPA. Oooh. This is very tempting. We seem to get the TGA O + FRI that we need, but we have to be very careful here. Remember, FRI stands for “far reaching influence ON THE ARTISTIC COMMUNITY.” Is that the same as “major influence on musicians?” Do musicians fully represent the artistic community? No. Furthermore, this answer choice adds in a third necessary element that is not mentioned in the original principle.

The correct answer is (B).

Only

From “If” to “Only If”

The word “only” could be the single most important word on the LSAT. It shows up all over the place. In the Logical Reasoning section of the exam, “only” is often a conditional logic trigger. To see how it comes into play, consider the following conditional statement:

Marcus wears a jacket if it is raining outside.

This is a pretty simple conditional relationship:

raining Marcus wears a jacket

In other words, the rain is enough, or sufficient, to trigger Marcus wearing a jacket. Anytime it rains, Marcus wears a jacket. We know by now that the reverse is NOT necessarily true: If Marcus wears a jacket, that doesn't necessarily mean that it is raining. Maybe he's wearing a jacket because it's cold out. Or maybe he's wearing a jacket because he's trying it on for size.

Now let's consider a slightly different statement:

Marcus wears a jacket only if it is raining outside.

Which one of the following is a correct interpretation of this new statement?

(A) If Marcus wears a jacket, then it is raining outside. (J R)
(B) If it is raining outside, then Marcus wears a jacket. (R J)

Well, we know that Marcus wears a jacket only when it rains outside. So, he can't wear a jacket under any other circumstance. Thus, IF he is wearing a jacket, THEN we know for certain it must be raining! J R. (A) is correct.

(B) is incorrect. Yes, Marcus wears a jacket only when it is raining (and no other time), but not necessarily every time it rains. R does not guarantee J. Let's review:

The standard conditional: Marcus wears a jacket if it is raining outside. (R J)
With “only if”: Marcus wears a jacket only if it is raining outside. (J R)

So, the “only if” gives us the exact opposite relationship. Note that replacing the word “if” with “when” gives us the same structures. “If” and “when” are equivalent:

Marcus wears a jacket when it is raining outside. (R J)
Marcus wears a jacket only when it is raining outside. (J R)

“If and Only If”?

Now let's take it one step further:

Marcus wears a jacket if, and only if, it is raining outside.

This is an LSAT favorite. It's a conditional construction that throws many test-takers for a serious loop. However, with a bit of thinking, we can make sense of this construction without much trouble. In fact, you already know all you need to know in order to properly interpret this statement. This statement is the combination of two simpler statements:

As you can see, the “if and only if” construction actually gives us two conditional statements, the second of which is simply the reverse of the first. Remember that each of these will yield a contrapositive. In the end, we get four relationships:

R J and the contrapositive –J –R
J R and the contrapositive –R –J

Another way to express the sum of these relationships is:

R J
–J –R

For “if and only if” statements, the arrows work in both directions. Here are some other terms that indicate this bidirectional relationship:

A if, but only if, B.	A when, and only when, B.
A then B, and only then.	All A, and only A, are B.

Time to get some practice interpreting the word “only.”

DRILL IT: Only

Choose all of the answer choices that are logically equivalent to the given statement. Keep in mind that there may be more than one correct answer for each question (or no correct answer at all!). Check your answers after each exercise.

Example (bold answers are correct):

If B, then A.

(A) B only if A.

(B) If A, then B.

(D) If not A, then not B. (the contrapositive!)

1. If Janet goes to the party, then Bill goes to the party.

(A) If Janet does not go to the party, then Bill does not go.

(B) Janet goes to the party only if Bill goes.

(D) If Bill does not go to the party, then Janet does not go.

2. The play is popular if ticket sales exceed 100.

(A) Ticket sales for the play exceed 100 only if the play is popular.

(B) Only if the play is popular do ticket sales for the play exceed 100.

(D) If the play is not popular, then ticket sales do not exceed 100.

3. Only if the car is new is it in good shape.

(A) The car is in good shape if, and only if, it is new.

(B) The car is new if, and only if, it is in good shape.

(D) If the car is new, then it is in good shape.

4. John speaks when, and only when, he is asked to speak.

(A) S AS, AS S

(B) –AS S

(D) –AS –S

5. Only the good die young.

(A) good die young

(B) –good –die young

(D) One who is not good never dies young.

SOLUTIONS: Only

1. If Janet goes to the party, then Bill goes to the party.

(A) If Janet does not go to the party, then Bill does not go.

(B) Janet goes to the party only if Bill goes.

(D) If Bill does not go to the party, then Janet does not go.

2. The play is popular if ticket sales exceed 100.

(A) Ticket sales for the play exceed 100 only if the play is popular.

(B) Only if the play is popular do ticket sales for the play exceed 100.

(C) If ticket sales exceed 100, then the play is popular.

(D) If the play is not popular, then ticket sales do not exceed 100.

3. Only if the car is new is it in good shape.

(A) The car is in good shape if, and only if, it is new.

(B) The car is new if, and only if, it is in good shape.

(C) If the car is in good shape, then it is new.

(D) If the car is new, then it is in good shape.

4. John speaks when, and only when, he is asked to speak.

(A) S AS, AS S

(B) –AS S

(C) –S –AS, –AS –S

(D) –AS –S

5. Only the good die young.

(A) good die young (Be careful. Only the good die young, but that doesn't mean ALL good people die young.)

(B) –good –die young

(C) One who dies young is good.

(D) One who is not good never dies young.

Applying Conditional Logic 3: Only, Must, and No

Here's an LSAT question that requires a strong understanding of what we just discussed. Give yourself 1:20 and then we'll go through it.

PT34, S2, Q10

Although the charter of Westside School states that the student body must include some students with special educational needs, no students with learning disabilities have yet enrolled in the school. Therefore, the school is currently in violation of its charter.

The conclusion of the argument follows logically if which one of the following is assumed?

(A) All students with learning disabilities have special educational needs.

(B) The school currently has no student with learning disabilities.

(D) The only students with special educational needs are students with learning disabilities.

(E) The school's charter cannot be modified in order to avoid its being violated.

Again, we're dealing with an Assumption question. Let's apply our approach:

DECISION #1: What is my task?

This question is asking us to select an assumption that would allow the conclusion to “follow logically.” In other words, we need a sufficient assumption.

DECISION #2: What is the author's conclusion?

DECISION #3: How is that conclusion supported?

Let's read the argument again with the above questions in mind:

Although the charter of Westside School states that the student body must include some students with special educational needs,

“Although” is a sign that we're about to get some contrary information.

no students with learning disabilities have yet enrolled in the school.

And here it is. The charter states that the student body must include some special needs students, but as of yet the school does not have any students with learning disabilities. Hmm. Notice the difference between the two concepts: “special needs students” and “students with learning disabilities.” Are these groups necessarily the same? We'll keep this in mind.

Therefore, the school is currently in violation of its charter.

This is obviously the conclusion. So the argument core is:

Charter requires SN students
+
no students with LD enrolled

school is in violation of its charter

DECISION #4: What is the gap?

We've already noticed the potential difference between special needs (SN) and learning disability (LD). If the school needs to have SN students to comply with its charter, and it doesn't have LD students, does that mean the school is in violation of the charter? There's something going on here with the connection between SN and LD. Our answer needs to address this.

DECISION #5: Which answer choices are clearly wrong?

The easiest eliminations will be answers that aren't related to the argument core. Here's our core again:

Charter requires SN students
+
no students with LD enrolled

school is in violation of its charter

(A) All students with learning disabilities have special educational needs.

This looks attractive. It makes a direct connection between LD and SN. Keep it for now.

(B) The school currently has no student with learning disabilities.

We already know this is true. This is one of our premises! This is a premise booster. Eliminate it.

This is tempting. It seems logical that they should enroll some special needs students. However, this isn't an assumption that would allow us to conclude that the school is currently in violation of the charter. Unless the argument is about what should or should not be done, be careful of answers that express “should's” or “should not's.” Eliminate it.

(D) The only students with special educational needs are students with learning disabilities.

Here's another one that seems to connect SN with LD. Better keep it for now.

(E) The school's charter cannot be modified in order to avoid its being violated.

This is out of scope. We're looking for an assumption that would allow us to conclude that the school is currently in violation of the charter. Whether the charter could be modified is irrelevant.

DECISION #6: What is the best available answer?

Okay, so we're down to two answers, (A) and (D), and they both look very good. When we're down to two, we always want to revisit the core before making a final decision.

Charter requires SN students
+
no students with LD enrolled

school is in violation of its charter

So, the argument assumes that if there are no LD, then there are no SN, right? We can express this in conditional form:

–LD –SN

Look at (A) one more time, and try to translate it into a conditional statement:

(A) All students with learning disabilities have special educational needs.

Don't read on until you've given it a shot. Does it match the assumption we've written above?

This translates to “All LD are SN.” (LD SN)

What do you think of (A) now? It's the exact negation of what we need! We need: –LD –SN. Back to (D):

(D) The only students with special educational needs are students with learning disabilities.

Don't continue on until you've tried to translate this statement. It's an “only” statement, so be careful. This is a difficult statement. Let's look at a simpler, more intuitive one that uses the same structure:

The only people who water ski are those who can swim.

We've got two choices, right? It's either W S, or S W. Which one is it? Well, consider it from the perspective of guarantees. Which one guarantees the other?

If you water ski, does that guarantee that you can swim? Yes, it does, because the only people who water ski are those who can swim.

If you can swim, does that guarantee that you water ski? No, it doesn't. A 5-year-old might be able to swim but not water ski. So, we have W S.

Back to (D) again.

(D) The only students with special educational needs are students with learning disabilities.

This is saying that the only students with SN are those who also have LD. In other words, if you have SN, then it is a guarantee that you also have LD:

SN LD

Oh no! This doesn't match our predicted assumption, –LD –SN, either! Or does it? Try taking the contrapositive of (D). This is the correct answer.

The key to this question is correctly interpreting the “only” conditional in answer choice (D). It's a tricky one. The more comfortable you get with the word “only,” the better off you'll be.

Beyond If/Then Triggers

We discussed the fact that “If/Then” phrasing indicates we're dealing with a conditional statement, but we also mentioned that disguised conditional statements won't contain the “If/Then” structure. For you to get the most out of your conditional logic knowledge on the LSAT, you'll need to learn to work with disguised conditionals. The key is the guarantee.

Looking for Guarantees

Have a look at this standard conditional statement:

If one is young, then one is happy.

According to this statement, being young guarantees happiness. Always. Without exception. Every time. We can express this exact idea in many different ways:

All young people are happy.
Being young assures happiness.
A young person is a happy person.

Each of these three statements conveys the exact same meaning as the original “If/Then” statement. Being young guarantees happiness. Always. Without exception. Every time. Thus, we can say these three statements are conditional statements, even though they may not look like it. When the LSAT gives us a conditional statement on a Logical Reasoning question, it will likely be disguised like this. How can we learn to recognize these disguised conditionals? We need to learn to recognize words that imply a guarantee. There are three main categories of such words. Here they are with examples for each. Notice that every disguised conditional statement can be translated to “If/Then” form:

1. Absolute modifiers (all, any, every, always, none, never)

All engineers enjoy math. (If one is an engineer, then one enjoys math.)

Any hamburger is worth $2. (If it is a hamburger, then it is worth $2.)

Every good movie has a star actor. (If it is a good movie, then it has a star actor.)

A new car always smells good. (If it is a new car, then it smells good.)

None of the pies at the party had blueberry filling. (If it was a pie at the party, then it did not have blueberry filling.)

Good soccer players are never good football players. (If one is a good soccer player, then one is not a good football player.)

2. Words of necessity (necessary, require, depend, assure, guarantee, must, is essential for)

A large vocabulary is necessary to be a great writer. (If one is a great writer, one has a large vocabulary.)

Success requires patience. (If a person is successful, then that person is patient.)

Being happy depends on being healthy. (If a person is happy, then that person is healthy.)

Repeated practice assures an error-free performance. (If one practices repeatedly, then one will have an error-free performance.)

Buying a ticket online guarantees a seat on the bus. (If one buys a ticket online, then one will have a seat on the bus.)

A good pizza must be hot. (If a pizza is good, then it is hot.)

Experience is essential for humility. (If one is humble, one has experience.)

3. Verbs of certainty (is, are, will be, do, do not, has/have)

A long story is a boring story. (If a story is long, then it is boring.)

Oranges are fruits. (If it is an orange, then it is a fruit.)

Mixing yellow and blue does not make red. (If yellow and blue are mixed, then red is not the result.)

Dogs have fleas. (If it is a dog, then it has fleas.)

This is certainly not an exhaustive list of words that imply a guarantee, but it is a start, and it should put you in the right mind-set for recognizing the clues when they are present. Let's give it a try. Take 1:20 for this one.

PT11, S2, Q9

Any announcement authorized by the head of the department is important. However, announcements are sometimes issued, without authorization, by people other than the head of the department, so some announcements will inevitably turn out not to be important.

The reasoning is flawed because the argument

(A) does not specify exactly which communications are to be classified as announcements

(B) overlooks the possibility that people other than the head of the department have the authority to authorize announcements

(D) assumes without warrant that just because satisfying a given condition is enough to ensure an announcement's importance, satisfying that condition is necessary for its importance

(E) fails to distinguish between the importance of the position someone holds and the importance of what that person may actually be announcing on a particular occasion

This is an Assumption Family question. Let's follow the steps:

DECISION #1: What is my task?

This question is asking us to find a flaw.

DECISION #2: What is the author's conclusion?

DECISION #3: How is that conclusion supported?

Let's read the argument again with the above questions in mind:

Any announcement authorized by the head of the department is important.

This could be a premise (statement of fact) or a claim (an opinion). Regardless, it's a disguised conditional statement, with the absolute modifier “any” being the clue. If an announcement is authorized by the head of the department, then the announcement must be important.

AHD I

(NOTE: Some people like to jot conditional statements down on the page in notation form, others don't. If you had trouble seeing that first sentence as a conditional, or if you generally prefer to work in diagram form, go ahead and get in the habit of putting conditionals on the paper using your own notation. It's fine if you choose not to write it down, as long as you can “hold” the logical information in your head as you continue reading.)

However, announcements are sometimes issued, without authorization, by people other than the head of the department,

Now, you've learned that “however” generally signals that the author disagrees with the part coming before it, but in this case “however” is not really used in the traditional way. It's used to introduce a contrast, not a difference in opinion.

Consider this analogous structure:

James empties the trash on Thursdays. However, Janet empties the trash on Fridays.

The “however” doesn't introduce a difference in opinion, but rather just a contrasting point. Important distinction!

So far we know that announcements authorized by the head of the department are important, and some announcements are NOT authorized by the head of the department:

AHD I
Some –AHD

so some announcements will inevitably turn out not to be important.

This is the conclusion. So the argument looks like this:

AHD I
Some –AHD Some –I

Another way to say this is:

AHD guarantees I.
So, –AHD means –I.

Do you notice anything fishy here? Try to figure it out before reading on.

DECISION #4: What is the flaw?

This argument presents a conditional relationship, and then concludes that the negation must also be true! Here's an analogy:

All children like ice cream. Bob is not a child. Thus, Bob does not like ice cream.

This doesn't make logical sense. It's perfectly reasonable that Bob could be an adult who likes ice cream. This argument illegally negates the logic of the conditional statement.

DECISION #5: Which answer choices are clearly wrong?

(A) does not specify exactly which communications are to be classified as announcements

Out of scope. The conclusion deals with the importance of certain announcements. This answer choice gives us nothing about importance. Eliminate it.

(B) overlooks the possibility that people other than the head of the department have the authority to authorize announcements

It's irrelevant whether other people have the authority to authorize announcements. What's important is whether an announcement can be deemed important when people who do NOT have authority issue these announcements. Remember, stay close to the conclusion. The conclusion is about the importance of unauthorized announcements. Our answer is bound to have the word “important” in it, one way or another.

We don't care if he/she never authorizes any announcements. Rather, we're interested in whether announcements that are not authorized are unimportant. Again, stay close to the conclusion.

(D) assumes without warrant that just because satisfying a given condition is enough to ensure an announcement's importance, satisfying that condition is necessary for its importance

I don't get it. Let's leave it for now.

(E) fails to distinguish between the importance of the position someone holds and the importance of what that person may actually be announcing on a particular occasion

The author does not fail to make this distinction. Furthermore, the importance of someone's position is irrelevant to this argument. Eliminate it.

DECISION #6: What is the best available answer?

There's only one answer left, (D). Let's evaluate how (D) actually expresses the flaw that we had anticipated. Let's review the anticipated flaw:

AHD guarantees I.
So, –AHD means –I.

The author negates the original conditional in order to draw a faulty conclusion. Now back to (D).

(D) assumes without warrant that just because satisfying a given condition is enough to ensure an announcement's importance, satisfying that condition is necessary for its importance

Wow! This is tough language! We can see that “assumes without warrant” is a fancy way of saying “assumes.” Now let's decode “…satisfying a given condition is enough to ensure an announcement's importance.” What given condition could they be talking about? Do we know of any condition that, when satisfied, would be enough to ensure an announcement's importance? Sure we do! We know that if an announcement is authorized by the head of the department, then it must be important! In other words, being authorized by the head is sufficient, or enough, to guarantee importance. AHD I.

So, the “satisfying a given condition” referred to in answer (D) is the authorization by the head of the department. Let's just substitute this into the answer choice and read it again:

(D) assumes without warrant that just because authorization by the head of the department is sufficient to ensure an announcement's importance, authorization by the head of the department is necessary for its importance

Now let's focus on the second part of the statement, the part after the comma: authorization by the head of the department is necessary for its (the announcement's) importance. If you get past the initial shock of the wording, this part is actually not so tough to decode—it clearly tells us which part is necessary!

So, answer (D) is really just saying this:

(D) assumes that because authorization by the head is sufficient for importance (AHD I), it must also be true that authorization by the head is necessary for importance (I AHD)

Answer (D) describes an illegal reversal of logic! We're almost there. Remember, the flaw that we spotted earlier on was that the argument illegally negates the logic:

AHD guarantees I.
So, –AHD means –I.

What we have in answer (D) is close:

AHD guarantees I.
So, I means AHD.

But once again, we've been provided the contrapositive of what was expected:

–AHD means –I = I means AHD.

So, to say that just because AHD is sufficient for importance means that AHD is necessary for importance is the same as saying the author makes an illegal reversal of a conditional statement, which is the same as saying the author makes an illegal negation of a conditional statement!

Phew! Tough problem! There's no way we could've gotten that without recognizing the disguised conditional in the argument, and without understanding the sufficient and necessary terminology used in answer choice (D).

Here's a general representation for you to study.

Let's say we have this argument:

X Y
Thus, Y X. (Which also means –X –Y, if you take the contrapositive.)

The author of this argument has:

Illegally reversed the logic.

Illegally negated the logic.

Confused a sufficient condition (X) for a necessary condition.

Confused a necessary condition (Y) for a sufficient condition.

Assumed that because X is sufficient to guarantee Y, it is also necessary for Y.

All five of these statements express the same overarching flaw. They all mean the same thing—the author made an invalid inference from a conditional statement. We tend to think and talk in terms of #1 and #2, but the LSAT will tend to use #3, #4, and #5 when writing answer choices.

Except Perhaps and Unless

Except Perhaps

It's time to discuss two of the most disguised conditional structures you'll see on the LSAT: except perhaps statements and unless statements. Take a look:

Javier arrives to work on time except perhaps if there is traffic.

We've learned that conditional statements are guarantees. This doesn't look much like a guarantee, does it? Well, think about it again. What do you know if there is NOT traffic? You got it. Javier arrives to work on time…guaranteed! So, if there is no traffic, Javier arrives to work on time.

NO traffic Javier arrives on time

This is what we call an “except perhaps” statement. Something, call it the normal state of affairs, always happens except perhaps when something else intrudes on the situation (call it the intruder). If the intruder does not occur, then we're guaranteed to have the normal state of affairs. Here's another example:

Gloria reads before bed except perhaps if there is something good on TV.

Normal state of affairs: Gloria reads before bed.
Intruder: Something good on TV.

If the intruder does not intrude, then we're assured to get the normal state of affairs:

NOT something good on TV Gloria reads before bed

Now, it's important that you don't fall into the “except perhaps” trap. The trap is to assume that if the intruder does intrude, you won't get the normal state. Here's how this would be written:

something good on TV Gloria does NOT read before bed

Note that this is an illegal negation of what we got earlier. It's wrong. Yes, the intruder is the only thing that can disrupt the normal state of affairs, but it doesn't necessarily disrupt the normal state. Say there was something good on TV. Perhaps Gloria would watch TV instead of reading, but just maybe she'd stick with her book if the book were particularly interesting. The operative word is perhaps. When the intruder intrudes, perhaps the normal state is affected, but not necessarily. Be careful!

So, here's the general formula for interpreting “except perhaps” statements:

Identify the normal state of affairs.
Identify the intruder.
Think: If the intruder does NOT intrude, we must get the normal state.
Write your conditional statement accordingly (NOT intruder normal state).

Try this one. Make sure you give it your best shot before reading on:

The Patriots will win the Super Bowl except perhaps if Tom Brady gets injured.

Normal state of affairs: Patriots will win the Super Bowl.
Intruder: Brady gets injured.
Think: If Brady does NOT get injured, we must get the normal state of affairs.
Conditional statement: Brady does NOT get injured Patriots win the Super Bowl

Don't fall for the trap. Note that if Brady does get injured, this doesn't necessarily mean the Patriots will lose. Maybe their backup quarterback will lead them to a win.

Unless

“Unless” statements are identical to “except perhaps” statements. They work exactly the same way:

Javier cannot be chosen for the position (guaranteed) unless he prepares for the interview (then maybe he can be chosen).

Normal state of affairs: Javier cannot be chosen.
Intruder: Preparation.
Think: If there is NO preparation, we must get the normal state of affairs.
Conditional statement: NO preparation Javier cannot be chosen.

Time to practice.

DRILL IT: Except Perhaps and Unless Statements

Translate the following statements into conditional notation. Be sure to check your answer after each exercise.

Example: Javier cannot be chosen for the position unless he prepares for the interview.

(–preparation –chosen)

1. Tommy cannot win the marathon except perhaps if Eugene drops out.

2. The carnival cannot proceed unless the clown gets better.

3. The car won't start except perhaps if we fill it with gas.

4. Jill does not carry the bucket unless Jack gets tired.

5. Unless the field dries, the game cannot be played.

SOLUTIONS: Except Perhaps and Unless Statements

1. Tommy cannot win the marathon except perhaps if Eugene drops out.

–Eugene drops out (or “Eugene races”) –Tommy wins

2. The carnival cannot proceed unless the clown gets better

–clown better –carnival proceed

3. The car won't start except perhaps if we fill it with gas.

–fill with gas –car start

4. Jill does not carry the bucket unless Jack gets tired.

–jack tired –jill carries bucket

5. Unless the field dries, the game cannot be played.

–dries –game played

Applying Conditional Logic 4: Unless Statements

It's time to test your knowledge. Give yourself 1:20, and then we'll discuss.

PT15, S3, Q7

Politician: Unless our nation redistributes wealth, we will be unable to alleviate economic injustice and our current system will lead inevitably to intolerable economic inequities. If the inequities become intolerable, those who suffer from the injustice will resort to violence to coerce social reform. It is our nation's responsibility to do whatever is necessary to alleviate conditions that would otherwise give rise to violent attempts at social reform.

The statements above logically commit the politician to which one of the following conclusions?

(A) The need for political reform never justifies a resort to violent remedies.

(B) It is our nation's responsibility to redistribute wealth.

(D) Economic injustice need not be remedied unless it leads to intolerable social conditions.

(E) All that is required to create conditions of economic justice is the redistribution of wealth.

This is an Inference question. We'll discuss Inference questions in a later chapter, but for now just know that an inference question basically requires us to choose an answer that we can prove from the given information in the passage. Note that this is NOT an Assumption Family question. We do not need to identify gaps or holes in the argument. Rather, we need to consider the information given, synthesize it, and then choose an answer that follows logically.

Many of you likely got this question correct without using any formal conditional logic. If the argument made sense to you, and you were able to anticipate the logical outcome, great! The conditional logic thought process we're about to demonstrate will give you a slightly different perspective on the question. If you weren't able to see the logical outcome, the conditional logic angle should help. Let's give it a shot. We'll start with the first sentence:

Politician: Unless our nation redistributes wealth, we will be unable to alleviate economic injustice and our current system will lead inevitably to intolerable economic inequities.

An “unless” statement! Let's break it down using the steps we outlined above:

Normal state of affairs: We will be unable to alleviate economic injustice and our current system will lead inevitably to intolerable economic injustice.

Intruder: Our nation redistributes wealth.

Think: If our nation does NOT redistribute wealth, then the normal state will occur.

Conditional statement: –redistribute economic injustice + intolerable economic inequities

If the inequities become intolerable, those who suffer from the injustice will resort to violence to coerce social reform.

Another conditional statement! This one is in standard “If/Then” form:

intolerable economic inequities violence

Notice that this conditional statement can be “hooked” onto the first one:

–redistribute economic injustice + intolerable economic inequities violence

In other words, if we don't redistribute, we'll end up with violence (follow the chain!):

–redistribute violence

It is our nation's responsibility to do whatever is necessary to alleviate conditions that would otherwise give rise to violent attempts at social reform.

So, we must do whatever we can to avoid violence. Well, if we don't want violence, we need to redistribute wealth. The contrapositive tells us as much:

–violence redistribute

Answer choice (B) is the correct answer that follows logically from the information given:

(B) It is our nation's responsibility to redistribute wealth.

Again, you may have arrived at (B) without resorting to conditional diagramming. That's okay. In fact, that's good. You should diagram the statements only when you're not able to make sense of the information in your head. It's kind of like asking someone for directions. We all resist writing them down, especially if they're easy to remember (like “drive to the river and make a left”), but as soon as they get complicated, we reach for a pen. That's the way you should think about conditional logic diagramming.

The Conditional Chain: Linking Conditional Statements

This last problem provides a good transition into the next section of the chapter. In our solution to the last question, we linked two conditional statements that shared a common element (intolerable economic inequities). Linking conditionals into a longer chain is crucial to getting the most out of your conditional logic knowledge on the LSAT. There are two basic types of linkages that you'll want to master:

1. The direct link.

Given: A B
Given: B C
The direct link: A B C
We can infer: A C

2. The contrapositive link.

Given: A B
Given: C –B
Take the contrapositive to get a like term: B –C
The link: A B –C
We can infer: A –C

Now, there's one type of invalid link that you will be tempted to make. Let's exorcise these temptations right here and now:

Given: A B
Given: A C
Temptation: B C

No, no, no! This is the equivalent of saying:

All apples are fruits. (A F)
All apples are red. (A R)
So, all fruits are red. (F R)

This doesn't work. In fact, there is no way to create a chain from this information, even after we try taking the contrapositives of the statements.

Let's practice making links.

DRILL IT: Conditional Chains

For each exercise, connect the pair of conditional statements into a chain. Some won't connect. Don't be tempted to jam them together! Be sure to check your answer after each exercise.

Example:

If you invite Aaron, Brian must be invited as well. If Chuck isn't invited, neither is Brian. A images

1. If Sam eats a piece of cake, he will not be hungry for dinner. If Jeremy bakes a cake, Sam will eat a piece of it.

2. If it's raining out, the picnic will be cancelled. Simone will be sad if the picnic is cancelled.

3. Every pianist knows the music of Bach. No one in my family knows the music of Bach.

4. A good apple is a ripe apple, and an apple will not be picked unless it is ripe.

5. Carrie is anxious when her dog misbehaves, and if Carrie is anxious, then her boyfriend is anxious as well.

6. Only troublemakers stay after school. All students who arrive late will stay after school.

7. Sarah apologizes only when she means it, and she always wears her purple sweater when she apologizes.

8. Being a good parent requires understanding and empathy. Those without experience cannot be empathetic.

9. Almost all flowers are pretty, and anything that is pretty is worth displaying in the home.

10. A wise person is never a talkative person, but every talkative person has something interesting to say.

11. Unless the street is dark, Jeffrey will walk home. The street is dark only on the weekends.

12. Tall trees require sunlight to survive. Tall trees get sunlight only when they are not blocked by other trees.

SOLUTIONS: Conditional Chains

1. If Sam eats a piece of cake, he will not be hungry for dinner. If Jeremy bakes a cake, Sam will eat a piece of it.

Jeremy bakes a cake Sam eats a piece of cake –Sam hungry for dinner

2. If it's raining out, the picnic will be cancelled. Simone will be sad if the picnic is cancelled.

raining picnic cancelled Simone sad

3. Every pianist knows the music of Bach. No one in my family knows the music of Bach.

in my family –know Bach –pianist

Or, perhaps you came up with a chain of contrapositives of the above:
pianist know Bach –in my family

Note that for each of these exercises, the contrapositives of the relationships are also correct.

4. A good apple is a ripe apple, and an apple will not be picked unless it is ripe.

good ripe
–ripe –picked

These can't be linked!

5. Carrie is anxious when her dog misbehaves, and if Carrie is anxious, then her boyfriend is anxious as well.

dog misbehaves Carrie anxious boyfriend anxious

6. Only troublemakers stay after school. All students who arrive late will stay after school.

arrive late stay after school troublemaker

7. Sarah apologizes only when she means it, and she always wears her purple sweater when she apologizes.

sarah apologizes sarah means it
sarah apologizes wears purple sweater

These can't be linked!

8. Being a good parent requires understanding and empathy. Those without experience cannot be empathetic.

–experience –empathy –good parent

9. Almost all flowers are pretty, and anything that is pretty is worth displaying in the home.

“Almost all” is not a guarantee!
pretty worth displaying

Don't worry, we'll talk about how to handle “almost,” “some,” and related terms later on.

10. A wise person is never a talkative person, but every talkative person has something interesting to say.

wise –talkative
talkative has something interesting to say

These cannot be linked!

11. Unless the street is dark, Jeffrey walks home from work. The street is dark only on the weekends.

–jeffrey walks home street dark weekend

12. Tall trees require sunlight to survive. Tall trees get sunlight only when they are not blocked by other trees.

tall trees survive sunlight –blocked by other trees

Applying Conditional Logic 5: Conditional Chains

Let's give it a try on a real one. Take a bit longer for this one, 1:40, so you can try approaching it using formal logic.

PT13, S2, Q10

Every political philosopher of the early twentieth century who was either a socialist or a communist was influenced by Rosa Luxemburg. No one who was influenced by Rosa Luxemburg advocated a totalitarian state.

If the statements above are true, which one of the following must on the basis of them also be true?

(A) No early twentieth century socialist political philosopher advocated a totalitarian state.

(B) Every early twentieth century political philosopher who did not advocate a totalitarian state was influenced by Rosa Luxemburg.

(C) Rosa Luxemburg was the only person to influence every early twentieth century political philosopher who was either socialist or communist.

(D) Every early twentieth century political philosopher who was influenced by Rosa Luxemburg and was not a socialist was a communist.

(E) Every early twentieth century philosopher who did not advocate a totalitarian state was either socialist or communist.

Notice that the two statements given in the original “argument” are facts. There is no conclusion. In fact, this is not an argument at all. This question is asking us to choose an answer that must be true based on the information in the text. This is another Inference question (again, we'll cover these in more detail later on).

The first word is “every,” a common conditional trigger. The start of the second sentence is “no one,” another absolute term that expresses a guarantee. So, both sentences in the passage are conditional statements. Most likely, we're going to need to connect the conditionals in order to draw an inference. Let's take it one step at a time. Take a minute to translate the first sentence into conditional terms:

Every political philosopher of the early twentieth century who was either a socialist or a communist was influenced by Rosa Luxemburg.

How would you convert this into standard “If/Then” form? Well, every socialist political philosopher (SPP) and every communist political philosopher (CPP) of the twentieth century was influenced by Rosa Luxemburg (IRL). So, if you were a SPP, then you were IRL. Furthermore, if you were a CPP, then you were IRL. Given the complex nature of this particular statement, it would be a good idea to get this down on paper.

SPP or CPP IRL

No one who was influenced by Rosa Luxemburg advocated a totalitarian state.

What about this one? Translate before reading on.

If you were IRL, then you did not advocate a totalitarian state (ATS):

IRL –ATS

Taking both of these together, the link should be clear!

SPP or CPP IRL –ATS

By making this connection we can infer a number of things:

SPP –ATS (and contrapositive: ATS –SPP)
CPP –ATS (and contrapositive: ATS –CPP)

We just need to be sure we can trace our abbreviations back to their actual meanings! Let's look at the answers:

(A) No early twentieth century socialist political philosopher advocated a totalitarian state.

If no SPP advocated a totalitarian state (ATS), then if you were an SPP, you did not ATS.

SPP –ATS

This is exactly one of the inferences we made by connecting the two conditionals. This is the correct answer.

(B) Every early twentieth century political philosopher who did not advocate a totalitarian state was influenced by Rosa Luxemburg.

We know that IRL –ATS. This was given to us. Answer (B) says –ATS IRL. An illegal reversal! While it might be true, we can't infer that it is true for certain. Eliminate it.

(C) Rosa Luxemburg was the only person to influence every early twentieth century political philosopher who was either socialist or communist.

We can't know if she was the only person. This is way too extreme. Eliminate it.

(D) Every early twentieth century political philosopher who was influenced by Rosa Luxemburg and was not a socialist was a communist.

We don't know this to be true from the information given. There could have been people who were influenced by Rosa but were not socialist OR communist.

(E) Every early twentieth century political philosopher who did not advocate a totalitarian state was either socialist or communist.

Perhaps there were political philosophers that were anarchists and who did not advocate a totalitarian state. From the stimulus, we didn't learn anything we can infer about –ATS.

Let's try another one. Same idea—1:40.

PT22, S4, Q25

Essayist: Every contract negotiator has been lied to by someone or other, and whoever lies to anyone is practicing deception. But, of course, anyone who has been lied to has also lied to someone or other.

If the essayist's statements are true, which one of the following must also be true?

(A) Every contract negotiator has practiced deception.

(B) Not everyone who practices deception is lying to someone.

(D) Whoever lies to a contract negotiator has been lied to by a contract negotiator.

(E) Whoever lies to anyone is lied to by someone.

This question asks us to find an answer choice that “must be true” based on the information given in the passage. Again, this is what we call an Inference question (to be discussed in greater detail later on).

Take a second and read through the paragraph again. Make a list of all the conditional triggers that you encounter. Don't read on until you've given it a shot.

Did you spot the following triggers?

Every
Whoever (meaning every person)
Anyone

Every piece of this paragraph contains conditional logic. Thus, we pretty much know that we can infer the correct answer from a conditional chain. We'll start by translating the conditional statements into arrow diagrams. (Again, if you were able to track the conditionals in your head, that's great. Seeing it written out should strengthen your understanding. If you weren't able to track the pieces mentally, then the diagram will certainly help.)

Every contract negotiator has been lied to by someone or other,

Contract negotiator has been lied to

and whoever lies to anyone is practicing deception.

Lie deception

But, of course, anyone who has been lied to has also lied to someone or other.

Has been lied to lied

Now take a second and see if you can make a chain. Remember, if you're given multiple conditionals, chances are you'll be able to connect them.

Contract negotiator has been lied to lied deception

So, this is saying that every contract negotiator has been lied to, which means every contract negotiator has lied to someone else, which means every contract negotiator has practiced deception!

Contract negotiator deception

Let's look at the answer choices:

(A) Every contract negotiator has practiced deception.

This is exactly the inference that we were able to draw above. This must be true, and so this is the correct answer.

(B) Not everyone who practices deception is lying to someone.

We know that if you lie to someone you are practicing deception: lie deception. But, we don't know if the reverse is true: deception lie. It may or may not be. It's not something we can determine for certain, so this is incorrect.

We know this is false. We know: lie deception. If you lie, you are practicing deception. Every time.

(D) Whoever lies to a contract negotiator has been lied to by a contract negotiator.

There's no way we can know this from our conditional chain.

(E) Whoever lies to anyone is lied to by someone.

We know: have been lied to lied, but we don't know the reverse!

Here's another one. This one is a Matching question (to be discussed in greater depth later) that uses conditional logic.

PT15, S2, Q18

Everyone who is a gourmet cook enjoys a wide variety of foods and spices. Since no one who enjoys a wide variety of foods and spices prefers bland foods to all other foods, it follows that anyone who prefers bland foods to all other foods is not a gourmet cook.

The pattern of reasoning displayed in the argument above is most similar to that displayed in which one of the following?

(A) All of the paintings in the Huang Collection will be put up for auction next week. Since the paintings to be auctioned next week are by a wide variety of artists, it follows that the paintings in the Huang Collection are by a wide variety of artists.

(B) All of the paintings in the Huang Collection are abstract. Since no abstract painting will be included in next week's art auction, nothing to be included in next week's art auction is a painting in the Huang Collection.

(C) All of the paintings in the Huang Collection are superb works of art. Since none of the paintings in the Huang Collection is by Roue, it stands to reason that no painting by Roue is a superb work of art.

(D) Every postimpressionist painting from the Huang Collection will be auctioned off next week. No pop art paintings from the Huang Collection will be auctioned off next week. Hence none of the pop art paintings to be auctioned off next week will be from the Huang Collection.

(E) Every painting from the Huang Collection that is to be auctioned off next week is a major work of art. No price can adequately reflect the true value of a major work of art. Hence the prices that will be paid at next week's auction will not adequately reflect the true value of the paintings sold.

Our goal for this question is to choose an answer that uses the same logic structure as the original argument. In this case, the original argument uses conditional logic. Let's translate statement by statement.

Everyone who is a gourmet cook enjoys a wide variety of foods and spices.

gourmet cook enjoys wide variety

Since no one who enjoys a wide variety of foods and spices prefers bland foods to all other foods,

enjoys wide variety –prefers bland foods

it follows that anyone who prefers bland foods to all other foods is not a gourmet cook.

prefers bland foods –gourmet cook

The two premises in this argument can be linked to form a three-part chain:

gourmet cook enjoys wide variety –prefers bland foods

From this, we can infer:

gourmet cook –prefers bland foods

Notice that the conclusion is simply the contrapositive of this statement:

it follows that anyone who prefers bland foods to all other foods is not a gourmet cook.

So the argument presents two premises that are linked to form a three-part chain, and the conclusion is simply the contrapositive:

A B C
So, –C –A

That's what we're looking for in our answer choice:

Huang paintings auction wide variety
Thus, Huang paintings wide variety

Did you get the relationship above? If so, be careful. This is misleading. Consider the following example:

All of the Dominguez children are at the party. Since the people at the party are of a wide variety of nationalities, the Dominguez children are of a wide variety of nationalities.

Dominguez children at party wide variety of nationalities

Does this mean: Dominguez children wide variety of nationalities? Of course not! The reason is that the conditional logic treats the group as a whole and not the individuals in that group. The same thing is happening with answer (A).

Besides, even if the conclusion were valid, it's not the contrapositive. We want an answer that uses a contrapositive.

Huang painting abstact –auction
So, auction –Huang painting

This is the same exact logic! This is the correct answer.

Huang painting superb
Huang painting –Roue
So, Roue –superb

In this case, the two premises cannot be linked, so the conclusion is invalid.

Postimpressionist Huang auction
Pop art Huang –auction
So, auction –Huang

We can link the premises to get:

Postimpressionist Huang auction –pop art Huang
So, pop art auction –Huang

This isn't the same structure.

Huang auction major work no price can reflect value

So, prices to be paid at auction will not reflect value.

None of the prices? Not even those paid for works other than Huang paintings? We can't know this. Furthermore, this doesn't use the contrapositive of the chain.

Linking Assumptions

Conditional logic is often used on Assumption questions. Here's a simple example:

Every child likes ice cream. Everyone who likes ice cream buys ice cream. Thus, every child is rich.

Hmm. Bad argument, right? Where did the “rich” come from? “Rich” seems to be the odd man out—we'll call it the “odd man.”

There's obviously a problem here.

Let's translate the conditionals into arrow notation. We'll start with the premises:

child likes ice cream
likes ice cream buys ice cream

And now the conclusion:

child rich

Just as we practiced, we can link the premises together. Look for the shared term and use that as the middle of your link. In this case, the shared term is “likes ice cream.”

child likes ice cream buys ice cream

Now, think. If the odd man, “rich,” were hooked to the end of the chain, we'd be able to go from “child” all the way across to “rich.”

child likes ice cream buys ice cream rich

But what did we need to assume in order to connect “rich” to the chain? We needed to assume “buys ice cream rich.” In other words, we needed to assume:

Anyone who buys ice cream is rich.

If we put this back into the argument we'll see that this is exactly the missing link that we needed:

Every child likes ice cream. Everyone who likes ice cream buys ice cream. (Anyone who buys ice cream is rich.) Thus, every child is rich.

Let's review the steps we took:

We recognized the conditional triggers. Since there were three conditional statements in the original argument, we knew we could attack this question by linking conditionals.
We translated the conditionals into arrow notation.
We linked the premises by linking the conditionals. Remember, look for the shared term and make that the middle of the linkage.
We hooked the “odd man” to the chain.
We identified the assumption by considering what we needed to link the odd man.

Let's try it on a real question. Give yourself 1:20 to answer, and then we'll discuss.

PT35, S1, Q14

Novelists cannot become great as long as they remain in academia. Powers of observation and analysis, which schools successfully hone, are useful to the novelist, but an intuitive grasp of the emotions of everyday life can be obtained only by the kind of immersion in everyday life that is precluded by being an academic.

Which one of the following is an assumption on which the argument depends?

(A) Novelists require some impartiality to get an intuitive grasp of the emotions of everyday life.

(B) No great novelist lacks powers of observation and analysis.

(D) Novelists cannot be great without an intuitive grasp of the emotions of everyday life.

(E) Knowledge of the emotions of everyday life cannot be acquired by merely observing and analyzing life.

Let's look at this question through two lenses. We'll start by approaching this question just as we would any other assumption question. Determine our task, find the core, spot the gap (if we can), eliminate answers not related to the core, and choose between the last men standing. We'll run through a quick, abbreviated version of this now.

Our task is to find a necessary assumption, so we'll need to begin by identifying the argument core:

An intuitive grasp of the emotions of everyday life can be obtained only by the kind of immersion in everyday life that is precluded by being an academic.

Academic novelists cannot become great.

In other words:

Academics can't immerse themselves in daily life, so they can't get an intuitive grasp of the emotions of everyday day life.

Academic novelists cannot become great.

Assumption: One who can't get an intuitive grasp of the emotions of everyday life can't be a great novelist.

(A) Novelists require some impartiality to get an intuitive grasp of the emotions of everyday life.

But can they be great without this intuitive grasp? This answer relates to the premise, but fails to connect to the conclusion. Eliminate it.

(B) No great novelist lacks powers of observation and analysis.

Okay, but what if they lack a grasp of everyday emotions? Can they be great then? This answer relates to the conclusion (being great), but fails to connect to the premise (intuitive grasp of emotions). Eliminate it.

Again, what about lacking an emotional grasp of everyday emotions? Eliminate it.

(D) Novelists cannot be great without an intuitive grasp of the emotions of everyday life.

This one relates the two concepts. Keep it for now.

(E) Knowledge of the emotions of everyday life cannot be acquired by merely observing and analyzing life.

Okay, but what about being great? This one references the premise but fails to tie in the conclusion.

Answer (D) is the correct answer.

How did you do? Did you successfully identify the core? Were you able to spot the gap between not having a grasp of the emotions of everyday life and not being a great writer? Were you able to eliminate at least some of the answer choices quickly? Did you get the right answer? Hopefully this type of question is beginning to feel comfortable for you.

Let's take another look at this question through the conditional logic lens. For those who got this question right the first time, this new perspective will strengthen your understanding of the logic. For those who struggled with this question, the conditional logic approach will allow you to see the inner workings of the logic in a way that perhaps you missed the first time. Here we go.

We'll look at the argument one more time, looking at each sentence in isolation to see if we can express it in conditional terms:

Novelists cannot become great as long as they remain in academia.

Believe it or not, this is a conditional statement. The big clue is the verb of certainty, cannot. Think about in terms of guarantees. Does being or doing one thing guarantee another? Indeed. Being an academic novelist guarantees that you will NOT be, or cannot be, a great novelist. In other words, if you are an academic novelist, then you are NOT a great novelist.

academic novelist –great novelist

Powers of observation and analysis, which schools successfully hone, are useful to the novelist,

This statement has no conditional structure, so let's leave it for now.

but an intuitive grasp of the emotions of everyday life can be obtained only by the kind of immersion in everyday life that is precluded by being an academic.

Did you spot the “only” trigger? An intuitive grasp of the emotions of everyday life can be obtained only by immersion in everyday life. Thus, if you are to have an intuitive grasp of everyday emotions, then you must immerse yourself in everyday life.

intuitive grasp of emotions immerse in everyday life

This sentence also contains a second conditional. Immersion in everyday life is precluded by being an academic. In other words, if you are an academic, you cannot immerse yourself in everyday life.

academic –immerse in everyday life

So, we have the following conditionals:

intuitive grasp of emotions immerse in everyday life
academic –immerse in everyday life

And these premises lead to the following conclusion:

academic novelist –great novelist

Next step, link them up! Notice that the shared term between the premises is “immerse in everyday life.” We'll want to use this as the middle of our chain. Also notice, however, that “immerse in everyday life” is positive in the first premise but negative in the second. We can't immediately link them this way. In order to get them both positive or both negative we'll need to take the contrapositive of one of them. Let's do the first one. So we'd get:

–immerse in everyday life –intuitive grasp of emotions
academic –immerse in everyday life

Now we can link them:

academic –immerse in everyday life –intuitive grasp of emotions

And these premises are used to support this conclusion:

academic novelist –great novelist

“Great novelist” is the odd man here. It appears only in the conclusion. Let's hook the odd man to the chain:

academic –immerse in everyday life –intuitive grasp of emotions –great novelist

Now we can see that “academic” leads to “-great novelist,” and the conclusion is now valid. But what did we need to assume in order to hook the odd man to the chain? We needed to assume:

–intuitive grasp of emotions –great novelist

In other words, if you don't have an intuitive grasp of emotions, you can't be a great novelist. This is exactly what answer (D) says:

(D) Novelists cannot be great without an intuitive grasp of the emotions of everyday life.

So, we looked at two ways to tackle this Assumption question. The first used our standard argument core approach, and the second used a conditional logic diagram approach. Ideally, you should be familiar with each of these methods.

Some and Most

Okay, we've spent the entire chapter harping on the idea that conditional statements express guarantees. We include a discussion of “some” and “most” here because “some” and “most” statements do NOT express guarantees, but they are often confused with conditional statements. Here's an example illustrating the difference:

All movies have a message. (movie message)

This means every movie. Every time. Always. No exceptions. Guaranteed.

Most movies have a message.

We might be tempted to write “movie message,” but “most” means “most,” NOT “all!” In other words, for any given movie, there's a good chance (more than half) that it will have a message, but it's NOT guaranteed.

Some movies have a message.

This is even less certain. “Some” simply means more than zero—at least one. “Some” is definitely not a guarantee.

If we can't treat “some” and “most” statements in the same way that we treat conditional statements, what do we do with them?

First, it's important to understand the context of “some” and “most” on the LSAT. Generally speaking, “some” and “most” statements are used most often on Inference questions (to be discussed in a later chapter). So, when learning how to deal with these statements, it's very important to think about these statements in terms of inferences. In other words, given a set of “some” and “most” statements, what can we infer? What can we conclude? What do we know for sure? Let's develop a set of rules that will come in handy in drawing valid inferences from “some” and “most” statements.

“Some” and “Most” Equivalents

The first step is to be able to recognize and understand the words and phrases that are synonyms of “some” and “most.” Here's a list of the most common:

Words and Phrases	Definition
some	one or more
most	more than half
a few	= some
majority	= most
nearly all	= most
many	= some

Single Statement Inferences

Next, we need to understand what sorts of inferences we can draw from a single “some” or “most” statement. Look at this:

Some teachers are musicians.

Can we reverse this statement? Indeed we can. If some teachers are musicians, then it must be true that some musicians are teachers (maybe not most or all, but definitely some). So, we have our first inference:

Original Statement	Inference
Some A's are B's.	Some B's are A's.

What about this one?

Most ice cream is delicious.

Can we reverse this one? We've purposely chosen a real-life statement to make it easier to consider. Think about it. Most ice cream is delicious. Are most delicious things ice cream? Of course not. There are zillions of delicious foods that are not ice cream. This statement cannot necessarily be reversed. The only thing we know for sure is that some delicious things (even if just a tiny fraction) are ice cream. This leads to our second inference:

Original Statement	Inference
Some A's are B's.	Some B's are A's.
Most A's are B's.	Some B's are A's.

Now let's look at this one:

All apples are fruits.

This sort of statement should be familiar—it's a conditional statement, a guarantee. All apples, every apple, every single one, is a fruit. We already know that we can NOT reverse this one, but we also know from this statement that some fruits must be apples:

Original Statement	Inference
Some A's are B's.	Some B's are A's.
Most A's are B's.	Some B's are A's.
All A's are B's.	Some B's are A's.

Not too bad, right? Now let's see what happens when we get more than one statement.

Multiple Statement Inferences

Suppose we had the following two statements:

Some people are happy.
Some people are old.

What can you infer? Can you infer that some happy people are old? Or that most happy people are old? Or maybe that all happy people are old? Let's use a diagram to figure this out. Assume that the box below represents all people:

All people

We know that some of these people are happy. Remember “some” means one or more. So, if we were going to shade part of the box to represent the happy people, how much would we shade? Well, it's unclear. It could be less than half, but it could also be more than half. We'll start with this—the stars will represent the happy people:

All people

We also know that some people are old. “Some” means one or more. Let's use circles to represent the old people:

All people

This is a valid representation of our statements, isn't it? Some are happy, and some are old. So what can we conclude? It seems from the picture that we would conclude that no happy people are old. In other words, the patterns don't overlap. Be careful though. Couldn't we have represented our statements like this?

All people

Or maybe even like this?

All people

The answer is yes. All three of these representations are accurate. Each one of them could be an actual representation of the statements. However, we don't know for sure that any of them represent the actual scenario, so we can't really conclude anything. Maybe none of them overlap (no old people are happy), maybe some of them overlap (some old people are happy), or maybe all of them overlap (all old people are happy). Without more information, we can't know for sure. This leads to our first overlap inference:

Original Statement	Overlap Type	Overlap Inference
Some A's are B's. Some A's are C's.	Some + Some	Can't infer anything about overlap between B and C. (They may or may not overlap.)

Let's look at two more statements:

Most people are happy.
Some people are old.

We can analyze this using the same thought process. “Most” means more than half, and “some” means one or more. We'll start by filling in “most” of the box with happy people:

Since we're dealing with a “most” statement, we need to be sure that more than half of the box is filled.

Take a second and think about how you could shade the box with old people. Remember, “some” people are old. There are actually a number of possibilities, aren't there? Here are three such possibilities:

Most people are happy (stars), and some people are old (circles). Do we know if they overlap? Well, they might (the right picture), but they might not (the left picture and the center picture). Perhaps all the old people are happy! We don't know for sure, so we can't infer anything about the overlap.

Original Statement	Overlap Type	Overlap Inference
Some A's are B's. Some A's are C's.	Some + Some	Can't infer anything about overlap between B and C. (They may or may not overlap.)
Most A's are B's. Some A's are C's.	Most + Some	Can't infer anything about overlap between B and C. (They may or may not overlap.)

One more combination:

Most people are happy.
Most people are old.

Now, set your watch for 2 minutes. Use this time to really think about what you can or cannot infer about the overlap of happy and old in this case. Use a box diagram if need be, and don't read on until you have an answer.

Again, we'll start by filling “most” of the box with happies:

“Most” people are also old. We'll need to fill “most” of the box with old people as well. There are a few ways we can do this:

All of these are valid, aren't they? In all three cases, more than half the box are stars, and more than half are circles. And, in every case, there is at least some overlap. Try to come up with a shaded scenario for which there is no overlap. You can't do it. (If you're having trouble seeing that, imagine there are only 10 people in the world; you'll need at least 6 happies and 6 oldies. Can you avoid an overlap?) When we combine two “most” statements, at least some will always overlap.

Original Statement	Overlap Type	Overlap Inference
Some A's are B's.	Some + Some	Can't infer anything about overlap between B and C. (They may or may not overlap.)
Some A's are C's.
Most A's are B's.	Most + Some	Can't infer anything about overlap between B and C. (They may or may not overlap.)
Some A's are C's.
Most A's are B's.	Most + Most	Some B's are C's.
Most A's are C's.

Got it? Time to practice.

DRILL IT: Some and Most

Choose the answer that must be true from the information given.

Some cars are sedans and some cars are red.
(A) Most cars that are sedans are red.

(B) Some things that are red are cars.

(C) None of the above.
Most people are patient and most people are sympathetic.
(A) Some sympathetic people are patient.

(B) Most patient people are sympathetic.

(C) None of the above.
Most children play sports, and some children play instruments.
(A) Some children who play instruments play sports.

(B) Some people who play sports are children.

(C) None of the above.
Many dogs weigh more than 20 pounds, and many dogs are difficult to train.
(A) Most dogs that weigh more than 20 pounds are difficult to train.

(B) Some dogs that are difficult to train weigh more than 20 pounds.

(C) None of the above.
The majority of flights arrive late, and few flights have empty seats.
(A) Some flights with empty seats arrive late.

(B) Most flights that arrive late have empty seats.

(C) None of the above.
Every ethical person succeeds, and some Americans are ethical.
(A) Some people who succeed are Americans.

(B) Most Americans succeed.

(C) None of the above.
Nearly all of Jason's books are fiction books, and all of Jason's books are written in Spanish.
(A) Most of Jason's books are fiction books written in Spanish.

(B) Most of Jason's books are not fiction books.

(C) None of the above.
Some children are happy, some children are healthy, and some children are smart.
(A) Some children are both happy and healthy.

(B) Some children are at once happy, healthy, and smart.

(C) None of the above.

Want more practice? Try playing “Ah-hah” in our LSAT Arcade. (www.manhattanprep.com/lsat/arcade)

Solutions: Some and Most

Choose the answer that must be true from the information given.

Some cars are sedans and some cars are red.
(A) Most cars that are sedans are red.

(B) Some things that are red are cars.

(C) None of the above.
Most people are patient and most people are sympathetic.
(A) Some sympathetic people are patient.

(B) Most patient people are sympathetic.

(C) None of the above.
Most children play sports, and some children play instruments.
(A) Some children who play instruments play sports.

(B) Some people who play sports are children.

(C) None of the above.
Many dogs weigh more than 20 pounds, and many dogs are difficult to train.
(A) Most dogs that weigh more than 20 pounds are difficult to train.

(B) Some dogs that are difficult to train weigh more than 20 pounds.

(C) None of the above.
The majority of flights arrive late, and few flights have empty seats.
(A) Some flights with empty seats arrive late.

(B) Most flights that arrive late have empty seats.

(C) None of the above.
Every ethical person succeeds, and some Americans are ethical.
(A) Some people who succeed are Americans.

(B) Most Americans succeed.

(C) None of the above.
Nearly all of Jason's books are fiction books, and all of Jason's books are written in Spanish.
(A) Most of Jason's books are fiction books written in Spanish.

(B) Most of Jason's books are not fiction books.

(C) None of the above.
Some children are happy, some children are healthy, and some children are smart.
(A) Some children are both happy and healthy.

(B) Some children are at once happy, healthy, and smart.

(C) None of the above.

Conclusion

We've covered a lot of tough material in this chapter. Here's a summary of the main points:

1. A standard conditional statement is expressed in “If/Then” form:

IF one is happy, THEN one is smiling.

2. The “IF” part of the statement is called the sufficient condition because it is sufficient on its own to guarantee the “THEN” part of the statement. The “THEN” part of the statement is called the necessary condition because it must be true when the sufficient condition is satisfied.

3. We can express conditional statements using arrow notation:

happy smiling

4. For any conditional statement, the contrapositive can be inferred. The contrapositive is found be reversing and negating the original statement:

–smiling –happy

5. There are four types of compound conditionals. Some can be split into two separate statements, others cannot:

AND in the Outcome (split):

If one is happy, then one is smiling AND cheerful.

happy smiling

happy cheerful

OR in the Trigger (split):

If one is happy OR cheerful, then one is smiling.

happy smiling

cheerful smiling

AND in the Trigger (can't split):

If one is happy AND cheerful, then one is smiling.

happy + cheerful smiling

OR in the Outcome (can't split):

If one is happy, then one is smiling OR cheerful.

happy smiling or cheerful

6. To take the contrapositive of a compound conditional statement, reverse and negate the terms, and swap AND for OR (or vice versa):

happy + cheerful smiling

–smiling –happy or –cheerful

party birthday or graduation

–birthday + –graduation –party

7. “Only” is one of the most important words on the LSAT. Watch out for “only if” and “if and only if” language:

Jenny smiles only if she is happy.

smiles happy

Jenny smiles if, and only if, she is happy.

smiles happy

8. Be on the lookout for words that express a guarantee. Words like always, never, every, anyone, everyone, etc. are generally used on the LSAT to express conditional relationships:

Every child likes chocolate.

child likes chocolate

9. “Except perhaps” and “unless” are used to express conditional statements:

The picnic will be canceled unless the sun comes out.

–sun comes out canceled picnic

10. Learn to link conditional statements to form a conditional chain:

A B
B C
So, A B C

11. “Some” and “most” are not “all!” Don't confuse “some” and “most” with conditional logic. Know your “some” and “most” rules—you'll need them on some Inference questions.

DRILL IT: Conditional Logic Questions

The following eight questions represent a mix of question types, some of which you have not yet studied. The common thread is that each question contains conditional logic. You will be forced to use your understanding of conditional logic in flexible ways, so don't get too mechanical! If you're still feeling shaky, do these untimed on another sheet of paper. Otherwise, give yourself about 11 minutes.

1. PT13, S2, Q9

In a mature tourist market such as Bellaria there are only two ways hotel owners can increase profits: by building more rooms or by improving what is already there. Rigid land-use laws in Bellaria rule out construction of new hotels or, indeed, any expansion of hotel capacity. It follows that hotel owners cannot increase their profits in Bellaria since Bellarian hotels _________.

Which one of the following logically completes the argument?

(A) are already operating at an occupancy rate approaching 100 percent year-round

(B) could not have been sited any more attractively than they are even in the absence of land-use laws

(C) have to contend with upward pressures on the cost of labor which stem from an incipient shortage of trained personnel

(D) already provide a level of luxury that is at the limits of what even wealthy patrons are prepared to pay for

(E) have shifted from serving mainly Bellarian tourists to serving foreign tourists traveling in organized tour groups

2. PT23, S2, Q9

Every action has consequences, and among the consequences of any action are other actions. And knowing whether an action is good requires knowing whether its consequences are good, but we cannot know the future, so good actions are impossible.

Which one of the following is an assumption on which the argument depends?

(A) Some actions have only other actions as consequences.

(B) We can know that past actions were good.

(D) Only actions can be the consequences of other actions.

(E) For an action to be good we must be able to know that it is good.

3. PT13, S2, Q26

If Blankenship Enterprises has to switch suppliers in the middle of a large production run, the company will not show a profit for the year. Therefore, if Blankenship Enterprises in fact turns out to show no profit for the year, it will also turn out to be true that the company had to switch suppliers during a large production run.

The reasoning in the argument is most vulnerable to criticism on which one of the following grounds?

(A) The argument is a circular argument made up of an opening claim followed by a conclusion that merely paraphrases that claim.

(B) The argument fails to establish that a condition under which a phenomenon is said to occur is the only condition under which that phenomenon occurs.

(C) The argument involves an equivocation, in that the word “profit” is allowed to shift its meaning during the course of the argument.

(D) The argument erroneously uses an exceptional, isolated case to support a universal conclusion.

(E) The argument explains one event as being caused by another event, even though both events must actually have been caused by some third, unidentified event.

4. PT23, S3, Q14

If the proposed tax reduction package is adopted this year, the library will be forced to discontinue its daily story hours for children. But if the daily story hours are discontinued, many parents will be greatly inconvenienced. So the proposed tax reduction package will not be adopted this year.

Which one of the following, if assumed, allows the argument's conclusion to be properly drawn?

(A) Any tax reduction package that will not force the library to discontinue daily story hours will be adopted this year.

(B) Every tax reduction package that would force the library to discontinue daily story hours would greatly inconvenience parents.

(C) No tax reduction package that would greatly inconvenience parents would fail to force the library to discontinue daily story hours.

(D) No tax reduction package that would greatly inconvenience parents will be adopted this year.

(E) Any tax reduction package that will not greatly inconvenience parents will be adopted this year.

Challenge Questions

5. PT14, S4, Q9

Since anyone who supports the new tax plan has no chance of being elected, and anyone who truly understands economics would not support the tax plan, only someone who truly understands economics would have any chance of being elected.

The reasoning in the argument is flawed because the argument ignores the possibility that some people who

(A) truly understand economics do not support the tax plan

(B) truly understand economics have no chance of being elected

(D) do not support the tax plan do not truly understand economics

(E) have no chance of being elected do not truly understand economics

6. PT24, S2, Q24

No mathematical proposition can be proven true by observation. It follows that it is impossible to know any mathematical proposition to be true.

The conclusion follows logically if which one of the following is assumed?

(A) Only propositions that can be proven true can be known to be true.

(B) Observation alone cannot be used to prove the truth of any proposition.

(D) Knowing a proposition to be true is impossible only if it cannot be proven true by observation.

(E) Knowing a proposition to be true requires proving it true by observation.

7. PT18, S2, Q23

Teachers are effective only when they help their students become independent learners. Yet not until teachers have the power to make decisions in their own classrooms can they enable their students to make their own decisions. Students’ capability to make their own decisions is essential to their becoming independent learners. Therefore, if teachers are to be effective, they must have the power to make decisions in their own classrooms.

According to the argument, each of the following could be true of teachers who have enabled their students to make their own decisions EXCEPT:

(A) Their students have not become independent learners.

(B) They are not effective teachers.

(D) They have the power to make decisions in their own classrooms.

(E) They do not have the power to make decisions in their own classrooms.

8. PT24, S3, Q10

All material bodies are divisible into parts, and everything divisible is imperfect. It follows that all material bodies are imperfect. It likewise follows that the spirit is not a material body.

The final conclusion above follows logically if which one of the following is assumed?

(A) Everything divisible is a material body.

(B) Nothing imperfect is indivisible.

(D) The spirit is perfect.

(E) The spirit is either indivisible or imperfect.

SOLUTIONS: Conditional Logic Questions

1. PT13, S2, Q9

Which one of the following logically completes the argument?

(A) are already operating at an occupancy rate approaching 100 percent year-round

(B) could not have been sited any more attractively than they are even in the absence of land-use laws

(C) have to contend with upward pressures on the cost of labor which stem from an incipient shortage of trained personnel

(D) already provide a level of luxury that is at the limits of what even wealthy patrons are prepared to pay for

(E) have shifted from serving mainly Bellarian tourists to serving foreign tourists traveling in organized tour groups

Answer choice (D) is correct.

We're facing an Inference question, which is not in the Assumption Family, so there's no core to find. We'll learn more about this question type later. Instead of a core, we're given a rule and asked to apply it. The rule is:

More hotel profits

more rooms or improving

The contrapositive is:

NOT more rooms and NOT improving

NOT more hotel profits

Then we're told that it's impossible to build more rooms, and thus hotel owners cannot increase their profits since _______________.

We're looking for something that completes this argument. If the conclusion is NOT more hotel profits, we can arrive at that by “triggering” the sufficient side of the contrapositive shown above. We already know that the hotels cannot build more rooms, so the argument will be valid if improvements to the hotels are also impossible.

(D) provides the other sufficient factor. If hotels are already providing the highest level of luxury possible (or at least what even the wealthy customers are willing to pay for), then the hotels cannot improve upon what already exists. Because of how it's phrased, this isn't an obvious answer, so understanding why the wrong answers are wrong comes in handy.

(A) is irrelevant to the argument. Full occupancy does not lead to “NOT more hotel profits.” Perhaps in the real world this would be relevant, but we're asked to complete the argument provided.

(B) is out of scope. Where the hotel is sited is irrelevant as far as the argument is concerned.

(C) is out of scope—the cost of labor is relevant in the real world, but it's not discussed in the argument. Furthermore, how much will the cost of labor rise? Will it become a problem?

(E) is completely irrelevant.

2. PT23, S2, Q9

Which one of the following is an assumption on which the argument depends?

(A) Some actions have only other actions as consequences.

(B) We can know that past actions were good.

(D) Only actions can be the consequences of other actions.

(E) For an action to be good we must be able to know that it is good.

Answer choice (E) is correct.

Let's look at this question using a formal conditional logic approach and then again using the core approach:

Formal Approach

Let's take this problem phrase by phrase:

Every action has consequences,

action

consequence

and among the consequences of any action are other actions.

consequence

action

So far we have a circular argument!

And knowing whether an action is good requires knowing whether its consequences are good,

know if action good

know if consequences good

but we cannot know the future, so good actions are impossible.

NOT know if future consequences good

good actions are NOT possible

Let's try to chain something to lead towards the conclusion, starting with NOT knowing future consequences are good:

NOT know if future consequences good

NOT know if good

And now we have to attach the conclusion somehow:

So what we're missing is

NOT know if good

good actions are NOT possible

Looking for an answer that might be a match, (A) through (D) do not include any reference to being good, but let's check (E):

(E) For an action to be good, we must be able to know that it is good.

action is good

know that the action is good

And the contrapositive:

NOT know that the action is good

action is NOT good

It's a match!

It turns out that the first conditional statement about every action having a consequence is not part of the chain we used to arrive at the conclusion. (However, it is important background that makes the complete argument valid since if not every action had consequences, then there could be good, though consequenceless actions that could not be evaluated.) This is why it's important to not be overly formal with formal logic! Keep your eye on the linkable premises and the conclusion.

Core Approach

The conclusion of this argument is that good actions are impossible. How sad. Support for this is provided in the beginning of that sentence: “we cannot know the future and thus whether consequences are good.” But why is that relevant? The first sentence provides the other premise: knowing whether an action is good requires knowing whether its consequences are good.

The core can be represented like this:

We have to know if consequences are good to know if an action is good.
+
We cannot know future (consequences)

Good actions are impossible.

With a bit of thinking, the two premises can be combined into one premise, leaving us with this core:

We cannot know if an action is good.

Good actions are impossible.

Did you notice the term shift? The premises are focused on whether an action or its consequences can be known to be good, while the conclusion is about whether a good action can be possible.

Scanning the answer choices, only (E) connects knowing whether an action is good and that action being good. If we negate (E)—this is a Necessary Assumption question, so the negation test applies here—we're left with an action can be good even if we don't know that it is good. If that were true, the argument would not make sense since good actions would be possible.

The wrong answers all fail to connect the premises to the conclusion.

(A) does not discuss actions being possible.

(B) similarly fails to connect to the conclusion. Furthermore, we are not concerned with past actions!

(C) is out of scope—the argument is not about whether one refrains from an action or what one knows if one refrains. It is flawed also because it doesn't discuss an action being good.

(D) does not discuss an action being good. Another premise booster (or premise confuser!).

Which approach is easier or faster? It's important to be judicious in using your formal logic notation—sometimes fancier isn't faster.

3. PT13, S2, Q26

The reasoning in the argument is most vulnerable to criticism on which one of the following grounds?

(A) The argument is a circular argument made up of an opening claim followed by a conclusion that merely paraphrases that claim.

(B) The argument fails to establish that a condition under which a phenomenon is said to occur is the only condition under which that phenomenon occurs.

(C) The argument involves an equivocation, in that the word “profit” is allowed to shift its meaning during the course of the argument.

(D) The argument erroneously uses an exceptional, isolated case to support a universal conclusion.

(E) The argument explains one event as being caused by another event, even though both events must actually have been caused by some third, unidentified event.

Answer choice (B) is correct.

This flaw question hinges on a flaw in conditional logic. The conclusion of this argument is actually a relationship: B.E. not profit B.E. switch suppliers. The support for this is a different relationship: B.E. switch suppliers B.E. not profit.

Notice something fishy? To boil it down further: –profit switch, because switch –profit. It's reversed logic!

(B) uses tricky language to describe this flaw. One way to unpack (B) is to consider what relationship added to switch –profit would allow us to conclude that –profit switch? We would need the reverse of the premise (giving us a bi-conditional): Blankenship Enterprises will not show a profit if, and only if, the company has to switch suppliers during a large production run (–profit sharing). The argument “acts” as if this added relationship exists—it assumes it.

Since answer (B) seems rather intimidating, let's decode each part:

The argument fails to establish…

The argument doesn't say…

that a condition under which a phenomenon is said to occur…

that not showing a profit because of switching suppliers (switch –profit)

is the only condition under which that phenomenon occurs…

is the only reason the company wouldn't show a profit (–profit switch).

Let's look at the other answer choices:

(A) is tempting because there is something wrong with the argument's logic, and the same elements are used repeatedly, which might feel circular. But this is not a circular argument in which the premise is restated as a conclusion. (Here's an example of a circular argument: Flying on planes is not dangerous, therefore one form of travel, flying, is not dangerous). It should be rather apparent if an argument is circular.

(C) is incorrect because there is no shifting of the meaning of “profit.” A shift in word meaning is rare on the LSAT, and is usually pretty noticeable.

(D) is not true; there's no indication that the year that the argument mentions is exceptional or isolated, and the conclusion is not particularly universal.

(E) is a flaw, but not of this argument. The support for the conclusion is a causal relationship, not simply two correlated events.

4. PT23, S3, Q14

Which one of the following, if assumed, allows the argument's conclusion to be properly drawn?

(A) Any tax reduction package that will not force the library to discontinue daily story hours will be adopted this year.

(B) Every tax reduction package that would force the library to discontinue daily story hours would greatly inconvenience parents.

(C) No tax reduction package that would greatly inconvenience parents would fail to force the library to discontinue daily story hours.

(D) No tax reduction package that would greatly inconvenience parents will be adopted this year.

(E) Any tax reduction package that will not greatly inconvenience parents will be adopted this year.

Answer choice (D) is correct.

This argument can be approached formally:

Therefore, tax NOT adopted.

How can this argument chain lead to the tax package NOT being adopted? The contrapositive of the chain leads to that:

To trigger this chain, we'd need to know that parents will not accept being inconvenienced. More specifically, as (D) states, no legislation that will inconvenience parents will be adopted. In other words, parents will not accept the original chain being triggered as they refuse to endure its final result.

(A) is out of scope since it is about tax reductions that do not discontinue story hours. Answer choice (A)’s logic, story hour adopted, is not helpful to the argument.

(B) is an extreme premise booster. We already know that –story hour inconvenience. It's irrelevant whether this is true for all tax reduction packages.

(C) is a bit confusing. When a statement is filled with negatives, try to restate it in the positive. We can rephrase answer (C) as, “Every tax reduction package that would inconvenience parents will force the end of story hours.” This is similar to (B). We already know what would happen if the proposed tax reduction package were to pass.

(E) is similar to answer (A). We aren't interested in tax reductions that do not inconvenience parents.

Challenge Problems

5. PT14, S4, Q9

The reasoning in the argument is flawed because the argument ignores the possibility that some people who

(A) truly understand economics do not support the tax plan

(B) truly understand economics have no chance of being elected

(D) do not support the tax plan do not truly understand economics

(E) have no chance of being elected do not truly understand economics

Answer choice (D) is correct.

This argument is best approached formally since the stimulus contains three conditional logic statements, and each answer choice is a conditional statement as well. Let's dig in:

Since anyone who supports the new tax plan has no chance of being elected,

support

NO chance

and anyone who truly understands economics would not support the tax plan,

understand econ.

NOT support

only someone who truly understands economics would have any chance of being elected.

chance

understand econ.

The last sentence is the conclusion. Let's see if we can link up the premises to make the conclusion correct. We'll start with the sufficient part of the conclusion:

chance

understand econ.

We can link the contrapositive of the first statement to that:

But there's no way to connect anything to NOT support or to understand econ. This is the flaw. It's assuming that NOT support understand econ., and this is what (D) points out by providing a counterexample (a situation in which there is both NOT support and NOT understand econ.).

Each of the other answer choices is a counterexample to a link that wouldn't complete the argument (and neither would their contrapositives).

(A) understand econ. support

(B) understand econ. chance

(E) NO chance understand econ

6. PT24, S2, Q24

No mathematical proposition can be proven true by observation. It follows that it is impossible to know any mathematical proposition to be true.

The conclusion follows logically if which one of the following is assumed?

(A) Only propositions that can be proven true can be known to be true.

(B) Observation alone cannot be used to prove the truth of any proposition.

(D) Knowing a proposition to be true is impossible only if it cannot be proven true by observation.

(E) Knowing a proposition to be true requires proving it true by observation.

Answer choice (E) is correct.

Math proposition can't be proven true by observation Math proposition can't be known to be true

With this problem, the core approach and a more formal approach are one and the same. The key is to notice the term shift. The premise is about proving something true by observation, while the conclusion is about something being known to be true. If you were reading like a debater, you may have thought, “Perhaps some things are known to be true though they cannot be proven true by observation (for example, provable through deduction).”

(E) fills this gap: know that proposition is true proving true by observation. Its contrapositive is: can't be proven true by observation can't know proposition to be true.

There are some very tempting wrong answers here:

(A) provides us this: propositions known to be true propositions proven true. This seems like what we need—it definitely has terms we saw in the argument. However, (A) is not specific about proving true “by observation.” Answer choice (A) may seem like a sufficient assumption since it is broader than what we need. However, the fact that something can't be proven true by observation does not mean that it cannot be proven true by some other means.

Consider this analogous flaw:

If you don't own some sort of vehicle, you can't move heavy furniture. So, since Peter doesn't have an SUV, he can't move the couch.

Perhaps Peter has a truck!

(B) connects observation and proving the truth of something. This is a premise booster. We already know that observation can't prove a mathematical proposition. Where's the connection to knowing something to be true?

(C) tells us that proposition proven true known to be true. This is the negation of what we need, (and, like (A), is not specific to proving true by observation).

(D) is tempting since it references proving by observation. But the logic is the reverse of what we need. The conditional logic in (D) is NOT knowing a proposition to be true NOT proven by observation. We need NOT proven true by observation NOT know proposition to be true.

7. PT18, S2, Q23

According to the argument, each of the following could be true of teachers who have enabled their students to make their own decisions EXCEPT:

(A) Their students have not become independent learners.

(B) They are not effective teachers.

(D) They have the power to make decisions in their own classrooms.

(E) They do not have the power to make decisions in their own classrooms.

Answer choice (E) is correct.

What a hairy looking question! But, when taken apart carefully, this one actually folds quite easily. First, let's notice that this is not an Assumption Family question. Here we're asked to apply an argument in order to find something that we can infer (prove) to be false. There's no flaw or assumption to uncover in the argument. Thus, we're not reading the argument like a debater; we're reading to grasp the rules. We can translate each sentence as follows:

Sentence 1: t. effective s. ind. learners

Sentence 2: (t. enables) s. decisions t. decisions

Sentence 3: s. ind. learning s. decisions

Conclusion: t. effective t. decisions

Notice that we've taken some liberty in paraphrasing, and that's both crucial and dangerous. In order to quickly boil down an argument to simple statements, we often have to reduce ideas like “the power to make decisions in their own classrooms” to “t. decisions,” but it's important to know that we may have lost some crucial details and that we may need to reconsider those details if we find multiple tempting answer choices.

Let's link up our statements. From the conclusion, we know that we can link all the way from t. effective to t. decisions. Indeed, it is possible:

t. effective s. ind. learners s. decisions t. decisions

The question asks us what cannot be possible if (t. enables) s. decisions. Looking at our chain, that's triggering our third element, requiring (i.e., triggering) all the elements that are down the chain. In this case, all that is required is t. make decisions, and so we know that (E) cannot be true.

All the wrong answers are either “upstream” on the chain, or are not even on it:

(A) offers something not even on the chain: s. NOT ind. learners.

(B) is similar: t. NOT effective.

(D) is t. make decisions, something that we can infer! But don't forget your mission—we need to find what CANNOT be true.

8. PT24, S3, Q10

All material bodies are divisible into parts, and everything divisible is imperfect. It follows that all material bodies are imperfect. It likewise follows that the spirit is not a material body.

The final conclusion above follows logically if which one of the following is assumed?

(A) Everything divisible is a material body.

(B) Nothing imperfect is indivisible.

(D) The spirit is perfect.

(E) The spirit is either indivisible or imperfect.

Answer choice (D) is correct.

Core Approach

material bodies NOT perfect

spirit is NOT material body

The gap here is that if something is imperfect, it can't be the spirit. Or, as (D) states, the spirit is perfect.

Formal Approach

material bodies (material bodies) divisible (material bodies) NOT perfect (material bodies) NOT spirit

We're asked to find a sufficient assumption. (D) provides us the link between the last two elements of the chain, specifically the contrapositive: spirit perfect (e.g., NOT imperfect).

Which is easier? It depends on you. The approaches were not very different because, as is often the case, the gap that the answer hinges upon is found in the final connection, which is essentially the core of the argument. In short, if you can get to the core of an argument, it's often faster than a more formal approach.

Looking at the wrong answers, none of them provide the right connection:

(A) provides a reversal of a relationship in the premise: divisible material.

(B) also provides a reversal of a relationship in the premise: imperfect divisible.

(C) tells us that spirit divisible. If that's true, then spirit is imperfect. This doesn't help the argument, it actually negates it!

(E) offers a choice: spirit NOT divisible or NOT perfect. If we knew that spirit is definitely NOT divisible, then we could conclude that spirit is not material (by applying the contrapositive of “All material bodies are divisible…”). However, we don't know that spirit is definitely NOT divisible, since it might be NOT perfect (it's an either/or statement!). If spirit were NOT perfect, we could not infer that spirit is immaterial; actually, we would be unable to infer anything about that using the given premises.