Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
SOLUTION
| p | q | ~p | ~q | p→q | ~q→~p | (p→q)↔(~q→~p) |
| T | T | F | F | T | T | T |
| T | F | F | T | F | F | T |
| F | T | T | F | T | T | T |
| F | F | T | T | T | T | T |
All the truth values in the last column are T. Hence, it is a tautology.
