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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 only if P is true and Q is false.
Contents
It may be written using logical notation as:
And is equivalent to:
Properties
falsehood-preserving: The interpretation under which all variables are assigned a truth value of "false" produces a truth value of "false" as a result of material nonimplication.
Symbol
The symbol for material nonimplication is simply a crossed-out material implication symbol. Its Unicode symbol is 8603 (decimal).
Rhetorical
"p but not q."
Boolean algebra
(A'+B)'
Computer science
Bitwise operation: A&(~B)
Logical operation: A&&(!B)