给定三个正整数x,y和z以及谓词,CORRRECT可以使用以下哪个选项?
P(x) = ¬(x=1)∧∀y(∃z(x=y*z)⇒(y=x)∨(y=1))
(A) P(x)为真意味着x是素数
(B) P(x)为真意味着x是除1以外的数字
(C) P(x)始终为真,与x的值无关
(D) P(x)为真意味着x具有正好除1和x之外的两个因子答案: (A)
解释:
So the predicate is evaluated as
P(x) = (¬(x=1))∧(∀y(∃z(x=y*z)⇒((y=x)∨(y=1))))
P(x) being true means x ≠ 1 and
For all y if there exists a z such that x = y*z then
y must be x (i.e. z=1) or y must be 1 (i.e. z=x)
It means that x have only two factors first is 1
and second is x itself.
This predicate defines the prime number.
资料来源:http://clweb.csa.iisc.ernet.in/rahulsharma/gate2011key.html
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