# Implies

From Maths

(Redirected from Logical implication)

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]