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Question
Which of the following statements is a tautology?
Options
(∼q ∧ p) ∧ q
(∼q ∧ p) ∧ (p ∧ ∼p)
(∼q ∧ p) ∨ (p ∨ ∼p)
(p ∧ q) ∧ (∼(p ∧ q))
MCQ
Solution
(∼q ∧ p) ∨ (p ∨ ∼p)
Explanation:
Since p ∨ ∼p ≡ T,
(∼q ∧ p) ∨ (p ∨ ∼p) ≡ (∼q ∧ p) ∨ T ≡ T
∴ (∼q ∧ p) ∨ (p ∨ ∼p) is a tautology.
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Tautology, Contradiction, and Contingency
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