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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
Solution
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| p | q | r | ∼ p | ∼ q | ∼ p ∧ q | q ∧ r | ⑥ ∧ ⑦ | ⑧ ∧ ⑤ |
| T | T | T | F | F | F | T | F | F |
| T | T | F | F | F | F | F | F | F |
| T | F | T | F | T | F | F | F | F |
| T | F | F | F | T | F | F | F | F |
| F | T | T | T | F | T | T | T | F |
| F | T | F | T | F | T | F | F | F |
| F | F | T | T | T | F | F | F | F |
| F | F | F | T | T | F | F | F | F |
Since the entries in the last column of the above truth table are all false, the given statement is a contradiction.
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