An implication is a logical construction that essentially tells us if one condition is true, then another condition must be also true. Formally it is written
which would be read “ implies ”, or “ therefore ”, or “if , then ” (to name a few).
Implication is often confused for “if and only if”, or the biconditional truth function (). They are not, however, the same. The implication is true even if only is true. So the statement “pigs have wings, therefore it is raining today”, is true if it is indeed raining, despite the fact that the first item is false.
In fact, any implication is called vacuously true when is false. By contrast, would be false if either or was by itself false (, or in terms of implication as ).
It may be useful to remember that only tells you that it cannot be the case that is false while is true; must “follow” from (and “false” does follow from “false”). Alternatively, is in fact equivalent to
The truth table for implication is therefore
|Date of creation||2013-03-22 11:53:00|
|Last modified on||2013-03-22 11:53:00|
|Last modified by||akrowne (2)|
|Synonym||conditional truth function|