Computer Dictionary of Information Technology

implies

(=> 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.