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请教:2005年上半年软件水平考试(高级)系统分析师上午(综合知识)试题真题试卷第1大题第25小题如何解答?

【题目描述】

在代数系统T,min>中,T为m,n 间的整数集合,mn,且T 包括m 和n,min为两个整数中取小者的运算,则T中存在逆元的元素有(58)。A.m

B.n

C.

D.没有存在逆元的元素

【我提交的答案】: C
【参考答案与解析】:

正确答案:B

答案分析:

解析:根据定义可知T 中存在么元n,按照逆元的定义,只有元素”存在逆元n,使得 min(n,n)=n。

什么是逆元?定义是什么呢?

参考答案
       幺元,也称单位元是集合里的一种特别的元,与该集合里的二元运算有关。当它和其他元素结合时,并不会改变那些元素。
    设代数系统<A,*>,*是定义在A上的一个二元运算,且e是A中关于运算*的么元。如果对于A中的一个元素a存在着A中的某个元素b,使得b*a=e,那么称b为a的左逆元;如果a*b=e成立,那么称b为a的右逆元;如果一个元素b,它既是a的左逆元又是a的右逆元,那么就称b是a的一个逆元。
  由此可知n是幺元,min(n,n)=n,则n的逆元就是n,m不存在逆元。故选B.


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