Which one of these first-order logic formula is valid?

GATE · 2007 · IT

1. A.

   ∀x(P(x) => Q(x)) => (∀xP(x) => ∀xQ(x))

2. B.

   ∃x(P(x) ∨ Q(x)) => (∃xP(x) => ∃xQ(x))

3. C.

   ∃x(P(x) ∧ Q(x)) <=> (∃xP(x) ∧ ∃xQ(x))

4. D.

   ∀x∃y P(x, y) => ∃y∀x P(x, y)

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