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.

(2009-10-28)

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Nearby terms: implication « implicit parallelism « implicit type conversion « implies » imply » import » imprecise probability

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