Question

已知集合M={x|x=3n，n∈Z}，N={x|x=3n+1,n∈Z}，P={x|x=3n-1,n∈Z}，且a∈M,b∈N,c∈P，设d=a-b+c，则

A.d∈M B.d∈N C.d∈P D以上都不对
答案是a=3n b=3k+1 c=3m-1
d=3n-3k+3m-2 =3n-3k+3m-3+1= 3(n-k+m-1)+1
但我唔明既然设了a=3n,点解唔设b系3n+1,C系3n-1

Answer 1

因为虽然M N P中的n都属于z，但a b c是三个集合中任意的三项，a b c中的n不一定相同。比如：a=3，b=4，c=2可以，但a=3，b=7，c=5也可以。n的取值在不同集合间不受影响，可任意取。

追问

那为什么 3(n-k+m-1)+1属于d∈N ？
n-k+m-1可能是负数

追答

因为n k m可取任何整数，说以(n-k+m-1)的值可以是任何整数。如果设这个数为n，d就刚好符合集合N，所以d∈N
即使n-k+m-1是负数，也是符合的，Z表示整数，包括负数，所以集合N中包含有负数

Answer 2

因为在本题中n的取值可以一样也可以不一样，他就像是函数中的x一样，只是代表一个变量而已，你要是都设成n的话，就表示他们三个中的自变量必须都只能去一样的值，故不够全面所以在综合写在一个式子离得话应分开写成不同的字母。

追问

那为什么 3(n-k+m-1)+1属于d∈N ？
n-k+m-1可能是负数

Answer 3

令e=a-b=3n-1
则d=e+c=3n-2=3n+1
选 B

Answer 4

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TEDA

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Based on the Football Association sources, WANG Jian-ying that Pacheco has by no means carried out his insulting gestures,Air Jordan After Game, if the National Security Martin (microblogging) offside, he was assistant referee created a gesture opponents offside, the results allow one to find out Pacheco eyeful. This inference WANG Jian-ying insulting the Portuguese the meaning with the outcomes from the middle finger to fight back. WANG Jian-ying ran the whereabouts of the fourth official complaint, which said this: "I have seen what he did." The effect,Air Jordan Women, so humiliating Pacheco sent off.

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