Which one of the following is NOT valid?

(A) ∀x(P(x) ∧ Q(x)) = ∀xP(x) ∧ ∀ xQ(x)
(B) ∃x(P(x) ∨ Q(x)) = &existxP(x) ∨ ∃xQ(x)
(C) ∀x(P(x) ∨ Q(x)) = ∀xP(x) ∨ ∀ xQ(x)
(D) ∃x(P(x) ∧ Q(x)) ≠ ∃xP(x) ∧ ∀ xQ(x)


Answer: (C)

Explanation: ∀x(P(x) ∨ Q(x)) = ∀xP(x) ∨ ∀ xQ(x)
This is not valid.

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