material nonimplication is the negation of implication. p⊅q
| p | q | ⊅ |
|---|---|---|
| T | T | F |
| T | F | T |
| F | T | F |
| F | F | F |
The Venn Diagram of "It's not the case that A implies B"
File:Johnston Diagram Not If a Then b.png
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.
"It's not the case that p implies q."