Which of the following predicate calculus statements is/are valid:

GATE · 1992 · CS · Question 2 subparts

1. A.

   (∀x) P(x) ∨ (∀x) Q(x) → (∀x) {P(x) ∨ Q(x)}

2. B.

   (∃x) P(x) ∧ (∃x) Q(x) → (∃x) {P(x) ∧ Q(x)}

3. C.

   (∀x) {P(x) ∨ Q(x)} → (∀x) P(x) ∨ (∀x) Q(x)

4. D.

   (∃x) {P(x) ∨ Q(x)} → ¬(∀x) P(x) ∨ (∃x) Q(x)

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