Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
SOLUTION
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| p | q | ~p | (p∨q) | ~(p∨q) | ~p∧q | ~(p∨q)∨(~p∧q) |
| T | T | F | T | F | F | F |
| T | F | F | T | F | F | F |
| F | T | T | T | F | T | T |
| F | F | T | F | T | F | T |
In the above truth table, the entries in columns 3 and 7 are identical.
∴ ~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
