Contrapositive
LSAT glossary · Logical Reasoning
Definition
The logically equivalent restatement of a conditional in which both terms are negated and their order is reversed: P → Q restated as ¬Q → ¬P. A conditional and its contrapositive always have the same truth value — they are two surface forms of one underlying rule. On the LSAT, writing the contrapositive of every conditional is non-negotiable, because the test routinely presents inferences from the contrapositive direction ("no one who is not great at solving mysteries can be police chief" = "police chief → great at mysteries"). The contrapositive is the engine of Modus Tollens.
Contrapositive in plain English
A contrapositive is a second, equally-true way of saying the same 'if-then' rule, made by flipping the two parts AND negating both. Take 'If it's a dog, then it's an animal' — its contrapositive is 'If it's NOT an animal, then it's NOT a dog,' which is obviously just as true. In shorthand, P rightarrow Q becomes neg Q rightarrow neg P, where the little neg just means 'not.' The magic is that a rule and its contrapositive are guaranteed to have the same truth — so the LSAT loves hiding the answer in the flipped version, and writing out the contrapositive of every 'if-then' statement is a non-negotiable habit for scoring high.
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