49. a) Show that ∀xP (x) ∧ ∃xQ(x) is logically equivalent

to ∀x∃y (P (x) ∧ Q(y)), where all quantifiers have

the same nonempty domain.

b) Show that ∀xP (x) ∨ ∃xQ(x) is equivalent to ∀x∃y

(P (x) ∨ Q(y)), where all quantifiers have the same

nonempty domain.

please anybody tell how to prove this logical equivalency ?