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X, Y are in a set which has property P that any real number between X, Y also be
X, Y are in a set which has property P that any real number between X, Y also be
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2025-02-23
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问题
X, Y are in a set which has property P that any real number between X, Y also belongs to the set, which of the following is the set having property P?
选项
A、real number between 0 and 1
B、all real number but not whole numbers
C、all whole numbers
D、all positive integers
E、all negative integers
答案
A
解析
题目中的that引导定语从句来修饰property P。意思是:X,Y在某一个集合,这个集合具有性质P:只要X,Y在集合中,X,Y之间的任何实数也属于这个集合。
如果选取X=1.2,Y=4.5,那么按照性质P,就必须是区间(1.2,4.5)内的所有元素都属于集合,但是B中明确指出整数2,3,4不属于这个集合,所以B其实并不具有性质P。
选项A:real number between 0 and 1是连续的实数,那么无论选取哪两个数,这两个数之间的所有数都是实数,所以A为正确答案。
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