Difference between revisions of "Implies"
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| − | The implies relation, denoted <math>A\implies B</math> or <math>B\impliedby A</math> where {{M|A\text{ and }B}} are statements of some sort means: | + | The implies relation, denoted <math>A\implies B</math> or <math>B\impliedby A</math> where {{M|A\text{ and }B}} are statements of some sort means<ref>https://en.wikipedia.org/w/index.php?title=Truth_table&oldid=667166695#Logical_implication</ref>: |
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'''Note:''' it is only not true that <math>A\implies B</math> when we have {{M|A}} but not {{M|B}} | '''Note:''' it is only not true that <math>A\implies B</math> when we have {{M|A}} but not {{M|B}} | ||
| + | ==See also== | ||
| + | * [[Contrapositive]] | ||
| + | |||
| + | ==References== | ||
| + | <references/> | ||
| + | |||
{{Definition}} | {{Definition}} | ||
Latest revision as of 13:36, 16 June 2015
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]
