If you're having trouble with understanding what a contrapositive is on the LSAT, then watch this short video and 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 in the answers. 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 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 look at another example.
English: If there is no traffic on the road then we will arrive on time.
Lawgic: no traffic –> on time
Try to apply the two step transformation process and write out the proper contrapositive.
English: If we will not arrive on time, then there is traffic on the road.
Lawgic: /on time –> traffic
It will take some getting used to but eventually, you'll see that despite the differences in these statements, they actually express the same thing.
Contrapositives are very useful for the LSAT. To get the contrapositive from a Lawgic statement, you “flip and negate.”
Did you find this mini-lesson and video on contrapositives helpful? If so, you should check out our online LSAT course. It has hundreds more videos like this that cover every part of the LSAT.