GATE | IT | 2005 | Discrete maths | Logic | Question 36

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Let P(x) and Q(x) be arbitrary predicates. Which of the following statements is always TRUE?

((∀x(P(x)∨Q(x))))⟹((∀xP(x))∨(∀xQ(x)))

(∀x(P(x)⟹Q(x)))⟹((∀xP(x))⟹(∀xQ(x)))

(∀x(P(x))⟹∀x(Q(x)))⟹(∀x(P(x)⟹Q(x)))

(∀x(P(x))⇔(∀x(Q(x))))⟹(∀x(P(x)⇔Q(x)))

This question is part of this quiz :

Propositional and First Order Logic.,Gate IT 2005
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