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Question
(p ⇒ q) ∩ (q ⇒ r) ⇒ (p ⇒ r) is ______.
Options
A tautology
A contradiction
A tautology and a contradiction
Neither tautology nor a contradiction
MCQ
Fill in the Blanks
Solution
(p ⇒ q) ∩ (q ⇒ r) ⇒ (p ⇒ r) is a tautology.
Explanation:
| p | q | r | p→q | q→r | p→r |
| T | T | T | T | T | T |
| T | T | F | T | F | F |
| T | F | F | F | T | F |
| T | F | T | F | T | T |
| F | F | F | T | T | T |
| F | F | T | T | T | T |
| F | T | T | T | T | T |
| F | T | F | T | F | T |
∴ (p→q) ∩ (q→r) ⇒ (p→r) is a tautology.
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Tautology, Contradiction, and Contingency
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