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