Contrapositive

The Contrapositive of a conditional statement "if $p$ then $q$" ($p \rightarrow q$) is "if not $q$ then not $p$" ($\neg q \rightarrow \neg p$).

A statement and its contrapositive are Logical Equivalence: one is true exactly when the other is. For example, "if it's raining, the ground is wet" has the contrapositive "if the ground is not wet, it's not raining".

It's easy to confuse with the converse ($q \rightarrow p$) and the inverse ($\neg p \rightarrow \neg q$), which are not equivalent to the original statement. The equivalence is the basis of Proof by Contrapositive. See also Propositional Logic.