Dicrete Math w Proofs Show step by step xP x xQx is logicall

(Dicrete Math w Proofs) Show step by step

xP (x) xQ(x) is logically equivalent to xy(P (x) Q(y))

where all quantifiers have the same nonempty domain

Solution

Assume xP (x) xQ(x)

for x either P(x) holds for all x OR Q(x) hold allx

= Either P(x) holds for all x OR Q(y) holds for y

which implies xy(P (x) Q(y))