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

Question

TuteeHUB · Accepted Answer

∀𝑥 ∀𝑦 (𝑥, ) → ∀𝑥 ∀𝑦 𝑃(𝑦, 𝑥)

TuteeHUB · Answer

∀𝑥 ∃𝑦 (𝑥, ) ↔ ∃𝑦 ∀𝑥 𝑅(𝑥, 𝑦)

TuteeHUB · Answer

(∀𝑥 [∃𝑦 (𝑥, ) → 𝑆(𝑥, 𝑦)]) → ∀𝑥∃𝑦 𝑆(𝑥, 𝑦)

TuteeHUB · Answer

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

1.	Which one of the following well - formed formulae is a tautology?
A.	∀𝑥 ∃𝑦 (𝑥, ) ↔ ∃𝑦 ∀𝑥 𝑅(𝑥, 𝑦)
B.	(∀𝑥 [∃𝑦 (𝑥, ) → 𝑆(𝑥, 𝑦)]) → ∀𝑥∃𝑦 𝑆(𝑥, 𝑦)
C.	[∀𝑥 ∃𝑦 (𝑃(𝑥, 𝑦) → 𝑅(𝑥, 𝑦)]↔[∀𝑥 ∃𝑦 (¬ 𝑃(𝑥, 𝑦) ∨ 𝑅(𝑥, 𝑦)]
D.	∀𝑥 ∀𝑦 (𝑥, ) → ∀𝑥 ∀𝑦 𝑃(𝑦, 𝑥)
Answer» D. ∀𝑥 ∀𝑦 (𝑥, ) → ∀𝑥 ∀𝑦 𝑃(𝑦, 𝑥)

Discussion