The Contrapositive

Have trouble with LSAT contrapositives? Watch this short video, then read the rest of the post.

CONTRAPOSITIVES WILL SAVE YOUR LIFE.

Contrapositives are a life-saver on the LSAT. Often, you’ll think you got an answer choice right. “Duh, they want me to infer that ‘All business school students are greedy.’ Hmm… but I don’t see it. WHAT IS GOING ON LSAT?!” Well, that’s because the right answer choice says “If you’re not greedy, you’re not a business school student.” See, same thing! I mean that too. Contrapositives are logically equivalent statements. You can think of them as being genetic twins. They’re the same.

So which one is the contrapositive? Actually, they each are the contrapositive of the other.

Consider this example.

English: All dogs are unselfish.
Lawgic: D –> /S
English: If something is selfish, then it’s not a dog.
Lawgic: S –> /D

First, let’s agree that these sentences say the exact same thing. Agreed? Good. D –> /S is the contrapositive of S –> /D just as much as S –> /D is the contrapositive of D –> /S. They’re contrapositives of each other. Just like twins. So what does “contrapositive” mean? It just means that you’re referring to the only other way in the Lawgic language of expressing that particular conditional relationship. See how that’s different from English? In English, there are myriad ways to express that idea. In Lawgic, there are two. They are called contrapositives of each other.

To get from one statement in Lawgic to its contrapositive, you apply a two step transformation process.

Step 1. Switch the two symbols around the arrow.
Step 2. Slap a negation sign on each symbol.
Step 3. There is no Step 3. It’s a two step process.

You have to remember that when you slap a negation onto a symbol that’s already negated, the negation goes away. Negating “not selfish” becomes “selfish.”

LET’S REVIEW
Contrapositives are very useful for the LSAT. To get the contrapositive from a Lawgic statement, you “flip and negate.”

Did you like this mini-lesson and video on contrapositives? If so, you should check out our online LSAT course. It has hundreds more videos like this that cover every part of the LSAT.

About J.Y. Ping

J.Y. has been teaching the LSAT since 2006 and has taught thousands of students. He is the founder of 7Sage and PreProBono, two organizations dedicated to making legal education more accessible. He graduated from Columbia University in 2007 where he studied Economics, Political Science, and Philosophy and holds a J.D. from Harvard Law School.

J.Y. highly encourages all LSAT students to review their logic games using 7Sage's Fool Proof Method and to sign up for 7Sage's free trial LSAT course.