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 | F | T | T | F | F |
| F | T | T | F | F | T | F | F | T |
| F | F | T | T | F | T | F | T | F |
Truth values in the last column are not identical. Hence, it is contingency.
