Implies

The implies relation, denoted

$$A\implies B$$ or $$B\impliedby A$$ where $A\text{ and }B$ are statements of some sort means:

A	B	$$A\implies B$$	A	B	$$A\implies B$$
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

$$A\implies B$$ when we have $A$ but not $B$

See also

• Contrapositive