百度作业网Show that quantified statements
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/08/19 12:40:28
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(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
∀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
Show that quantified statements
quantified 或是 quantitative
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