Let P(x) and Q(x) be arbitrary predicates. Which of the following statements…

GATE · 2005 · 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))⟹∀x(Q(x)))⟹(∀x(P(x)⟹Q(x)))

4. D.

   (∀x(P(x))⇔(∀x(Q(x))))⟹(∀x(P(x)⇔Q(x)))

Attempted by 188 students.