Logical Reasoning: Inference Questions and the Contrapositive

A while ago, I did a brief post covering one simple format for formal logic inference questions in the LSAT's Logical Reasoning section.

However, they can follow a variety of formats - not simply that particular one.

In this blog post, I'll cover another common type of inference question - one in which the stimulus first sets up a conditional statement. The stimulus then provides us with a clause that activates the sufficient condition of the contrapositive of the previously-provided conditional statement.

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I know that was a mouthful.

What do I mean?

Suppose a Logical Reasoning stimulus is composed of a conditional statement, like X -> Y, as well as the additional information, NOT Y.

We can then take the contrapositive of that conditional statement, NOT Y -> NOT X, and plug in the additional information of NOT Y to spit out the result, NOT X.

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Must Be True Example

This is all a bit abstract, but let's look at it with an example from a real LSAT Logical Reasoning question, a Must Be True question:

(Please see PrepTest 30 (December 1999 LSAT), Section 2, Question 20 - page 59 in Next 10 to follow along. Due to copyright law, I'm unable to reproduce the text of the question itself.)

This stimulus begins with a claim made by critics saying (paraphrased):

If continued public funding is justified, then there must be some indication of public benefit.

We can diagram their claim with the following symbols:

CPFJ -> IPB

The stimulus continues by saying that if the critics' claim is true, then there would not be tremendous public support.

We can diagram this statement with the following symbols:

"CPFJ -> IPB" -> NOT TPS

Rather than using the word "NOT", I'd probably draw it instead like this:




I placed the critics' claim in quotes to indicate that the truth of their conditional statement's claim is serving as the sufficient condition of another conditional statement - the one with the necessary condition being (paraphrased), "then there would not be tremendous public support."

However, it doesn't simply say then there wouldn't be tremendous public support - it says, there wouldn't be all the tremendous public support that we do, in fact, have.

In other words, we DO have tremendous public support (diagrammed as):

TPS

As such, we can now take the contrapositive of the big conditional statement we just talked about:

"CPFJ -> IPB" -> NOT TPS

If there is tremendous public support, then the critics' claim that "in order for continued public funding to be justified, we must have an indication of public benefit" is NOT correct.

In other words, if we have tremendous public support, then an indication of public benefit is not necessary in order for continued public funding to be justified.

We can diagram this as:

TPS -> NOT "CPFJ -> IPB"

Again, rather than using the word "NOT", I'd probably draw it instead like this:




Since we do have tremendous public support, then we can conclude that the critics 'claim is not correct.

NOT "CPFJ -> IPB"

Choice E of this question pretty much says just that.

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Recommended assignment:

Now go through this process with another Logical Reasoning question that follows a similar format. I recommend PrepTest 31 (June 2000 LSAT), Section 3, Question 22 - page 101 in Next 10.