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