Material nonimplication

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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 P does not imply Q.

It may be written using logical notation as:

p⊅q
Lpq
p↛q

Definition[edit]

Truth table[edit]

p q ~\nrightarrow
T T F
T F T
F T F
F F F

Properties[edit]

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[edit]

The symbol for material nonimplication is simply a crossed-out material implication symbol. Its Unicode symbol is 8603 (decimal).

Natural language[edit]

Grammatical[edit]

Rhetorical[edit]

"It's not the case that p implies q."
"p but not q."

Colloquial[edit]

"Just because p, doesn't mean q."

Boolean algebra[edit]

(A'+B)'

Computer science[edit]

C: (A&(~B))

See also[edit]

References[edit]