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