GATE Computer Science (CS) 2015 Shift 2 Solved Paper

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Question : 63 of 65

Marks: +1, -0

Which one of the following well - formed formulae is a tautology?

∀𝑥 ∃𝑦 (𝑥, ) ↔ ∃𝑦 ∀𝑥 𝑅(𝑥, 𝑦)
(∀𝑥 [∃𝑦 (𝑥, ) → 𝑆(𝑥, 𝑦)]) → ∀𝑥∃𝑦 𝑆(𝑥, 𝑦)
[∀𝑥 ∃𝑦 (𝑃(𝑥, 𝑦) → 𝑅(𝑥, 𝑦)]↔[∀𝑥 ∃𝑦 (¬ 𝑃(𝑥, 𝑦) ∨ 𝑅(𝑥, 𝑦)]
∀𝑥 ∀𝑦 (𝑥, ) → ∀𝑥 ∀𝑦 𝑃(𝑦, 𝑥)

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