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