 Material nonimplication

Material nonimplication or abjunction (latin ab = "from", junctio =–"joining") is the negation of implication. That is to say that for any two propositions P and Q, if P does not imply Q, then P is the material nonimplication of Q.
It may be written using logical notation as:

 p⊅q
 Lpq
 p↛q
Contents
Definition
Truth table
p q T T F T F T F T F F F F Properties
falsehoodpreserving: 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 crossedout material implication symbol. Its Unicode symbol is 8603 (decimal).
Natural language
Grammatical
Rhetorical
"It's not the case that p implies q."
"p but not q."Colloquial
"Just because p, doesn't mean q."
Boolean Algebra
(A'+B)'
Computer Science
C: (A&(~B))
See also
Logical connectives This mathematical logicrelated article is a stub. You can help Wikipedia by expanding it. This logicrelated article is a stub. You can help Wikipedia by expanding it. 