Material nonimplication
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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 |
[edit] Definition
[edit] Truth table
| p | q | ⊅ |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | F |
[edit] 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)
[edit] 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.
[edit] Symbol
[edit] Natural language
[edit] Grammatical
[edit] Rhetorical
"It's not the case that p implies q."
"p but not q."
[edit] Colloquial
[edit] Boolean Algebra
[edit] Computer Science
[edit] See also
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