- 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 T T F T F T F T F F F F
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.
The symbol for material nonimplication is simply a crossed-out material implication symbol. Its Unicode symbol is 8603 (decimal).
"It's not the case that p implies q."
"p but not q."
"Just because p, doesn't mean q."
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