implication ⇝

implies

<logic>

(=> or a thin right arrow) A binary Boolean function and logical connective. A => B is a true implication unless A is true and B is false. The truth table is 

 A B | A => B
 ----+-------
 F F |   T
 F T |   T
 T F |   F
 T T |   T
It is surprising at first that A => B is always true if A is false, but if X => Y then we would expect that (X & Z) => Y for any Z.

If A is actually an expression X & Y then the implication is called a syllogism.

Last updated: 2009-10-28

Nearby terms:

implicit parallelism ♦ implicit type conversion ♦ implies ♦ imply ♦ import

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