Implies
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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:
| 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]
