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