Show that quantified statements∀x(P(x)⊕Q(x)) and (∀xP(x))⊕(∀xQ(x))are not logically equivalent.(证明两者不等)

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Show that quantified statements∀x(P(x)⊕Q(x)) and (∀xP(x))⊕(∀xQ(x))are not logically equivalent.(证明两者不等)
x) /W(H,Q(,M+LLMQ(.I,IM+)VS070Ш|55Hi*$(Ɂ$5``UE y% 9ɉ99 e9@s_o|6Ɏ%/Z}N"}Bna`NfpًuΟl'v=rv : [^,\|ɮ )ہ:K7D(DΆgs:JuLaCΙtޗf#WtEDgS[il 1nx*(df*+dAf1"X"Fz{

Show that quantified statements∀x(P(x)⊕Q(x)) and (∀xP(x))⊕(∀xQ(x))are not logically equivalent.(证明两者不等)
Show that quantified statements
∀x(P(x)⊕Q(x)) and (∀xP(x))⊕(∀xQ(x))
are not logically equivalent.(证明两者不等)

Show that quantified statements∀x(P(x)⊕Q(x)) and (∀xP(x))⊕(∀xQ(x))are not logically equivalent.(证明两者不等)
论域是人的集合,P(x)表示x是男人,Q(x)表示x女人,
∀x(P(x)⊕Q(x)) 表示所有人或是男人或是女人,是真命题
(∀xP(x))⊕(∀xQ(x))表示所有人是男人或所有人是女人,是假命题
故∀x(P(x)⊕Q(x)) and (∀xP(x))⊕(∀xQ(x))
are not logically equivalent

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