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Question
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p → q) ∧ (q → r)) → (p → r)
Solution
| p | q | r | p → q | q → r | p → r | (p → q) ∧ (q → r) | ((p → q) ∧ (q → r)) → (p → r) |
| T | T | T | T | T | T | T | T |
| T | T | F | T | F | F | F | T |
| T | F | T | F | T | T | F | T |
| T | F | F | F | T | F | F | T |
| F | T | T | T | T | T | T | T |
| F | T | F | T | F | T | F | T |
| F | F | T | T | T | T | T | T |
| F | F | F | T | T | T | T | T |
All the entries in the last column are only T.
∴ The given statement is a tautology.
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