A contrapositive of a statement is always true, assuming that the conditional statement is true. However, if the conditional statement is false, then the contrapositive is also false.

A conditional statement is usually expressed as

If P, then Q.

The contrapositive statement is usually expressed as

If not Q, then not P.

where P denotes a condition and Q denotes another condition.


Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".

See also