### 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 | TIt 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

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