Contrapositive

Definition

Given the statement [ilmath]A\implies B[/ilmath] (see implies) the contrapositive of this is: [ilmath]¬B\implies ¬A[/ilmath]

Proof:

[ilmath]A[/ilmath]	[ilmath]B[/ilmath]	[ilmath]A\implies B[/ilmath]	[ilmath]¬A[/ilmath]	[ilmath]¬B[/ilmath]	[ilmath]¬B\implies ¬A[/ilmath]
		T	T	T	T
	T	T	T		T
T				T
T	T	T			T

So as can be seen:

• [math][A\implies B]\iff[¬B\implies ¬A][/math]

For example see the definition of: Injection

See also

• Implies