2. Contrapositive

We just studied if A, then B. The contrapositive is if you reverse and negate that.

If momma bear crosses the river, so does baby bear. Contrapositive: If the baby didn’t cross, then momma didn’t, either.

Those who contrapose will do well on the GMAT (contrapose: the act of making a contrapositive). Why? You can take conditional rules and double them by contraposing the original conditional.

Original Conditional

Step 1:
Reverse Values

Step 2:
Negate Values to make Contrapositive

Two Valid Conditionals

And, poof!, it becomes two valid conditionals after you contrapose the original (reverse the statements and negate them).



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Here’s a minor diversion into pop culture and formal logic.

1) It don’t mean a thing if it ain’t got that swing.

~has swing → ~mean anything
Contrapositive: means anything → has swing

2) You must take the A Train,
If you want to go to Harlem.

go to Harlem → take the A train
Contrapositive: ~take the A train → ~go to Harlem

Contrapositive Drills

All non-professionals in the program use software to improve their driving.

If I don’t get into law school, then I plan on going to business school.

If you want to become a doctor than you shouldn’t smoke.

“No one can make you feel inferior without your consent.”
-Eleanor Roosevelt

Contrapositive of Quote

Contrapositive shown in red.


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“No one can be at peace unless he has his freedom.”
-Muhammed Ali

Contrapositive of Quote


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