Inverse (logic)

In logic, if S is a statement of the form P implies Q then the inverse of S is a statement of the form (not P) implies (not Q).

S and its inverse are not logical equivalents. For example, let S be the true statement "If I am a human, then I am mortal." The inverse of S is the statement "If I am not a human, then I am not mortal," which is not necessarily true.

A truth table makes it clear that S and the inverse of S are not logically equivalent:

See also: Converse, Contrapositive, Denying the antecedent.