# Implies

(Redirected from Logical implication)

The implies relation, denoted $A\implies B$ or $B\impliedby A$ where [ilmath]A\text{ and }B[/ilmath] are statements of some sort means[1]:

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 [ilmath]A[/ilmath] but not [ilmath]B[/ilmath]