Which of the following logic statements are valid?
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Which of the following predicate logic statements is/are valid?

(1) <math>\forall (x) P(x) \vee \forall(x)Q(x) \implies \forall (x) (P(x) \vee Q(x))</math>

(2) <math>\exists (x) P(x) \wedge \forall(x)Q(x) \implies \exists (x) (P(x) \wedge Q(x))</math>

(3) <math>\exists (x) (P(x) \vee Q(x)) \implies \forall (x) P(x) \vee \forall (x) Q(x)</math>

(4) <math>\exists (x) (P(x) \vee Q(x)) \implies \sim \forall (x) </math>

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Which of the following predicate logic statements is/are valid?[edit]

(1) <math>\forall (x) P(x) \vee \forall(x)Q(x) \implies \forall (x) (P(x) \vee Q(x))</math>

(2) <math>\exists (x) P(x) \wedge \forall(x)Q(x) \implies \exists (x) (P(x) \wedge Q(x))</math>

(3) <math>\exists (x) (P(x) \vee Q(x)) \implies \forall (x) P(x) \vee \forall (x) Q(x)</math>

(4) <math>\exists (x) (P(x) \vee Q(x)) \implies \sim \forall (x) </math>