# Contrapositives

Demon Team

Sep 20, 2023

No need to 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 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 use contrapositives on the LSAT?

Many LSAT courses and prep books teach contrapositives. Some even claim they’re “essential” to mastering Logic Games and 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.

On Logic Games, use worlds to deal with conditional rules. If the game says, “If A is fifth, then B is sixth,” make one world where A is fifth and B is sixth. Then, make another world where A is not fifth and so the rule doesn’t apply. Bam. The rule is now fully incorporated into your setup, and you never have to think about it again. Common sense trumps gimmicky diagramming strategies every time.

If you’re ready to ditch the dogma and learn the LSAT the easy way, start drilling questions from every official LSAT