Contraposition

Definition

Contraposition

Contraposition replaces an implication with its contrapositive: it negates both formulas and reverses their order. For formulas $A$ and $B$,

$$A⟹B⟺\neg B⟹\neg A.$$

The two implications have the same truth value: if $B$ is false, then $A$ must be false whenever

$$A⟹B$$

holds.