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