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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
implies
implication
imply
(=> 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)