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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[1]:

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