material nonimplication is the negation of implication. p⊅q
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" (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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