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Question
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
(p → q) ∧ (p ∧ ∼q)
Solution
| p | q | ∼q | p → q | p ∧ ∼q | (p → q) ∧ (p ∧ ∼q) |
| T | T | F | T | F | F |
| T | F | T | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | 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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