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