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LSAT Contrapositive

This is the third in a series of articles about LSAT Formal Logic. In this article we’ll get some practice in using the contrapositive to get some easy points on the LSAT Test.

This lesson series covers the following articles:

LSAT Formal Logic: An Introduction
LSAT If-Then Statements
LSAT Contrpositive 
Best LSAT Logic Tip

LSAT Contrapositive

Forming the contrapositive can get you quick points on the LSAT. Not only will you get the point right, but you’ll save a lot of time you can use later when you tackle the hard questions. Take a look at the following question:

Mary: My company doesn’t respect my time. I am expected to work long hours and weekends with no extra compensation given for my hard work. If I don’t get a raise by Tuesday, I’m quitting.

Which one of the following can be inferred from Mary’s statements?

(A)    Mary’s company is understaffed.
(B)    If Mary is still working after Tuesday, she got a raise.
(C)    If Mary gets a raise, she’s going to keep working long hours.
(D)    If Mary quits after Tuesday, she must not have received a raise.
(E)    If Mary continues to work weekends, she will quit soon.

First, by reading the question before reading the stimulus, you know you are looking for an inference. Second, as you read the stimulus, the conditional if-then statement should jump out at you. You know what to do with these statements — paraphrase them and figure out the contrapositive:

Paraphrase: If no raise, then quit (not R –> Q)

Contrapositive: Not quit, then raise (not Q –>R)

Now you know you’re looking for a situation where Mary doesn’t quit. That is the antecedent of the contrapositive. Now that you’ve made your prephrase, quickly scan the first parts of the answer choices.

Answers (B) and (E) are the only choices that start with Mary not quitting. See how much time you saved already? By forming the contrapositive and scanning for an answer choice that starts out right, you narrowed it down to two choices right off the bat. 

(B) looks just like the contrapositive. If Mary is still working after Tuesday, she must have received her raise. (E) is not so strong. Mary continues to work, but no mention is made of a raise. If this were the actual test, you should mark (B) and move on. Choice (B) is the contrapositive, so it has to be correct. Why waste time reading the other choices? Because this isn’t the actual test, however, and you need as much practice as possible, let’s consider the other choices.

(A) is out of scope. The argument never talks about staffing.

Choice (C) denies the antecedent. We know that this is a fallacy, so it cannot be right. Mary said that she would quit if she didn’t get a raise. But that doesn’t mean that she won’t quit for some other reason even if she does get a raise.

Choice (D) affirms the consequent. We know this is a fallacy, so it must be wrong. Again, there could still be other reasons why Mary would want to quit, even if she gets a raise.

Let’s try another one:

In order to hold a holiday parade, the city council must pass a resolution to close off Main Street. Rigby’s Department Store will certainly close early if shoppers cannot access Main Street.

Which one of the following can be inferred from the above?

(A) If Rigby’s is closed, Main Street must be closed.
(B) If Main Street is closed, there will be a parade.
(C) If Rigby’s Department Store is open, there will be a holiday parade.
(D) There is no holiday parade on any day that Rigby’s Department Store is open.
(E) Rigby’s Department Store hires the parade’s Santa Claus for the parade, so if Rigby’s Department Store is closed, there could not be a holiday parade.

We know from the question stem that we are looking for an inference. The argument is fairly short and despite it’s initial appearance, it is somewhat formal. You might paraphrase the argument in a more formal fashion like this:

Paraphrase: If parade, then Main Street closed. If Main Street closed, then Rigby’s closed.

Another way to paraphrase: parade –> MS closed –> Rigby’s closed.

You can see that “Main Street closed,” is common to both sentences, so we can create a quick chain like the last paraphrase. If I were writing the LSAT Test, I would try to be as tricky as possible and take the contrapositive of the whole chain. If Rigby’s is open, then there must not be a parade. So scan the answer choices for anything that contains Rigby’s open or no parade. (C) and (D) fit the bill.

Answer choice (C) starts out right, but ends wrong. Answer (D) is the correct choice.

Answer (A) and (B) both affirm different consequents. There might be other reasons that Rigby’s or Main Street would close besides a parade and we would still be consistent with the argument stimulus.

Answer (E) gives us wacky, out of scope information that we cannot use.

In the next article, we’ll discuss the Best LSAT Logic Tip you should learn.