Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
SOLUTION
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| p | q | ~p | ~q | p∧q | ~(p∧q) | ~p∨~q |
| T | T | F | F | T | F | F |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | F | T | T |
In the above table, entries in columns 6 and 7 are identical.
∴ Statement ~(p ∧ q) and ~p ∨ ~q are equivalent.
