Negative Disjunctive
Negative Disjunctive ~(p v q)
Read as "neither p nor q".
The negative disjunctive operator says that if either of the terms (p and q) is true, or both of them are true, then the statement is false. Thus only when both p and q are false is the statement true.
| p | q | ~(p v q) | Comments |
| T | T | F | Both terms are true so the statement is false since neither of them can be true for the statement to be true. |
| T | F | F | One term is true so the statement is false. |
| F | T | F | One term is true so the statement is false. |
| F | F | T | Neither term is true so the statement is true. |
Derivation
| p | q | p v q | ~(p ^ q) |
| T | T | T | F |
| T | F | T | F |
| F | T | T | F |
| F | F | F | T |
