The contrapositive of a conditional statement is written by negating both the hypothesis $q$ and the conclusion $p$ of the converse of the conditional statement. A contrapositive statement is written in if-then form.

Interchanging the hypothesis and the conclusion of the inverse statement can also form the contrapositive of the conditional. Consider the following conditional statement and its related conditionals.

	Example	Symbols
Conditional	$\text{If }\underset{p}{\underbrace{\text{a figure is a square}}},\text{then }\underset{q}{\underbrace{\text{it has four sides}}}.$	$p\Rightarrow q$
Converse	$\text{If }\underset{q}{\underbrace{\text{a figure has four sides}}},\text{then }\underset{p}{\underbrace{\text{it is a square}}}.$	$q\Rightarrow p$
Inverse	$\text{If }\underset{\neg p}{\underbrace{\text{a figure is }\text{not}\text{ a square}}},\text{then }\underset{\neg q}{\underbrace{\text{it does }\text{not}\text{ have four sides}}}.$	$\neg p\Rightarrow \neg q$
Contrapositive	$\text{If }\underset{\neg q}{\underbrace{\text{a figure does }\text{not}\text{ have four sides}}},\text{then }\underset{\neg p}{\underbrace{\text{it is }\text{not}\text{ a square}}}.$	$\neg q\Rightarrow \neg p$

The truth table of a contrapositive statement is made using the truth values for its hypothesis $\neg q$ and conclusion $\neg p.$

The contrapositive of a conditional statement has the same truth table as the conditional statement. In other words, a conditional and and its contrapositive are either both true or both false. Therefore, they are equivalent statements.