Material nonimplication

Material nonimplication or abjunction (latin ab = "from", junctio =–"joining") is the negation of material implication. That is to say that for any two propositions P and Q, the material nonimplication from P to Q is true if and only if not P implies Q. This is more naturally stated as that the material nonimplication from P to Q is true is only true if P is true and Q is false.