kenneth h rosen chapter 1 section section 1.5 nested quatnifiers excercise 49

Question

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 ?

Comments

Try Question 49 , section 1.4 . You will get the answer for this as well.