Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q
SOLUTION
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p | q | ~q | p→~q | ~(p→~q) | ~(~q) | p∧~(~q) | p∧q |
| T | T | F | F | T | T | T | T |
| T | F | T | T | F | F | F | F |
| F | T | F | T | F | T | F | F |
| F | F | T | T | F | F | F | F |
In the above table, entries in columns 5, 7, and 8 are identical.
∴ ~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q
