Contrapositives: What they are and why you don’t need to worry about them on the LSAT

Don’t spend valuable study time going down the rabbit hole of logical contrapositives. Here’s a quick, easy breakdown of what they are and why you don’t need them on the LSAT.

What’s a contrapositive?

A Contrapositive statement is the logical equivalent of a conditional (“if–then”) statement that you get by switching the sufficient and necessary conditions and negating both of them.

Here’s a simple example:

Conditional: If A, then B
Contrapositive: If not B, then not A

And another one:

Conditional: If it’s raining, then the grass is wet.
Contrapositive: If the grass isn’t wet, then it’s not raining.

A conditional statement and its contrapositive say essentially the same thing—they’re like two sides of the same coin.

Where does the concept come from?

Contrapositives didn’t come from the LSAT—the term never even appears on the test. Contrapositives have a long history in formal logic and mathematics. Both math and logic use contrapositives to prove the validity of concepts or theorems, for example, in geometry proofs.

Should you study contrapositives for the LSAT?

Many LSAT courses and prep books teach contrapositives. Some even claim they’re “essential” to mastering Logical Reasoning. But contrapositives by themselves can’t simplify games or increase understanding of arguments. More often, they confuse students and waste time.

Conditional statements are easier to grasp when you have an intuitive understanding of sufficient and necessary conditions. And while the LSAT doesn’t explicitly test contrapositives, sufficient and necessary are some of the most commonly tested LSAT concepts. Many students use contrapositives as a crutch, needlessly diagramming without actually understanding the original statement.

There’s an easier way to unlock conditionals in LSAT Logical Reasoning—ditch the diagramming, and go for real understanding. Let’s look at an example (Test J, Section 3, Q22):

If the price it pays for coffee beans continues to increase, the Coffee Shoppe will have to increase its prices. In that case, either the Coffee Shoppe will begin selling noncoffee products or its coffee sales will decrease. But selling noncoffee products will decrease the Coffee Shoppe’s overall profitability. Moreover, the Coffee Shoppe can avoid a decrease in overall profitability only if its coffee sales do not decrease.

The question then asks us to find what Must Be True.

This setup is overcomplicated and unhelpful when looking at the answer choices.

A) If the Coffee Shoppe’s overall profitability decreases, the price it pays for coffee beans will have continued to increase.

B) If the Coffee Shoppe’s overall profitability decreases, either it will have begun selling noncoffee products or its coffee sales will have decreased.

C) The Coffee Shoppe’s overall profitability will decrease if the price it pays for coffee beans continues to increase.

D) The price it pays for coffee beans cannot decrease without the Coffee Shoppe’s overall profitability also decreasing.

E) Either the price it pays for coffee beans will continue to increase or the Coffee Shoppe’s coffee sales will increase.

The quickest way to the correct answer is to understand the passage in commonsense terms. If the bean price increases, we know that coffee prices will too, which leads to selling non-coffee products or sales decreasing. Either of those things leads to profitability decreasing. Once we can simplify the passage down to this relationship, we don’t need to worry about contrapositives to figure out the answer.

A and B are out—they get the relationship backwards. D is out because the passage doesn’t mention anything about the price of beans decreasing. E is out because the passage doesn’t mention coffee sales increasing.

That leaves us with the correct answer, C, which captures the chain of events simply and correctly. If the price of beans increases, we know the final result will be profitability decrease. Boom.

If you’re ready to ditch the dogma and start learning the LSAT the easy way, head over to LSAT Demon to drill questions from every official LSAT.

More on Contrapositives

What is a contrapositive on the LSAT?

A contrapositive or contrapositive statement on the LSAT is the logical equivalent of a conditional statement that you get by switching the sufficient and necessary conditions and negating both. However, while contrapositives have a long history in formal logic and mathematics, they're not explicitly tested on the LSAT. Instead, understanding sufficient and necessary conditions intuitively is more effective for tackling LSAT questions, as contrapositives often complicate rather than simplify the reasoning process.

Is the contrapositive important?

The contrapositive is essential in mathematics for proving theorems, but on the LSAT, it's less important because the test focuses more on understanding sufficient and necessary conditions intuitively, rather than relying on complex logical transformations that can often confuse more than clarify.