Material nonimplication 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
- p↛q
Contents |
Definition
Truth table
| p | q | ⊅ |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | F |
Venn diagram
The Venn Diagram of "It's not the case that A implies B", or simply "A and not B" (the red area is true)
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
Natural language
Grammatical
Rhetorical
"It's not the case that p implies q."
"p but not q."
Colloquial
Boolean Algebra
Computer Science
See also
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