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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]
Solution
| p | q | ~p | ~q | p∨q | ~(p∨q) | ~(p∨q)→p | (~p)∧(~q) | [~(p∨q)→p]↔[(~p)∧(~q)] |
| T | T | F | F | T | F | T | F | F |
| T | F | F | T | T | F | T | F | F |
| F | T | T | F | T | F | T | F | F |
| F | F | T | T | F | T | F | T | F |
All the truth values in the last column are F. Hence, it is a contradiction.
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