(=> 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.