Implies

The implies relation, denoted [math]A\implies B[/math] or [math]B\impliedby A[/math] where [ilmath]A\text{ and }B[/ilmath] are statements of some sort means:

A	B	[math]A\implies B[/math]	A	B	[math]A\implies B[/math]
false	false	true			T
false	true	true		T	T
true	false	false	T
true	true	true	T	T	T

Note: it is only not true that [math]A\implies B[/math] when we have [ilmath]A[/ilmath] but not [ilmath]B[/ilmath]

See also

• Contrapositive