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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(p ∨ q) ∧ ∼p] ∧ ∼q
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Solution
| p | q | ∼p | ∼q | p ∨ q | (p ∨ q) ∧ ∼p | [(p ∨ q) ∧ ∼p] ∧ ∼q |
| T | T | F | F | T | F | F |
| T | F | F | T | T | F | F |
| F | T | T | F | T | T | F |
| F | F | T | T | F | F | F |
All the entries in the last column of the above truth table are F.
∴ [(p ∨ q) ∧ ∼p] ∧ ∼q is a contradiction.
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