contrapositive

A contrapositive statement is statement derived from a conditional by reversing and negating its antecedent and consequent. Thus the contrapositive of the conditional statement ‘if \(A\) then \(B\)’ is ‘if not \(B\) then not \(A\).’ In symbolic logic this is written as \(\neg B \rightarrow \neg A\).

A conditional and its contrapositive are logically equivalent; each is true precisely when \(B\) is true or \(A\) is false.