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Question
Examine whether the following statement pattern is a tautology or a contradiction or a 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 | F | T | F |
| F | F | T | T | T | T |
The entries in the last column of the above truth table are neither all T nor all F.
∴ (p ↔ q) ∧ (p → ∼ q) is a contingency.
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