implies definition 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
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