Contraposition

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In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent negated and swapped. Conditional statement P → Q {\displaystyle P\rightarrow Q} . In formulas: the contrapositive of P → Q {\displaystyle P\rightarrow Q} is ¬ Q → ¬ P {\displaystyle \neg Q\rightarrow \neg P} . If P, Then Q. — If not Q, Then not P. "If it is raining, then I wear my coat." — "If I don't wear my coat, then it isn't raining." The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true. Contraposition ( ¬...

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