Contrapositive

Definition

Given the statement $A\implies B$ (see implies) the contrapositive of this is: $¬B\implies ¬A$

Proof:

$A$	$B$	$A\implies B$	$¬A$	$¬B$	$¬B\implies ¬A$
		T	T	T	T
	T	T	T		T
T				T
T	T	T			T

So as can be seen:

• $$[A\implies B]\iff[¬B\implies ¬A]$$

For example see the definition of: Injection

See also

• Implies