Let R be the relation on Z×Z ,that is elements of this relat

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/07/14 15:55:59

Let R be the relation on Z×Z ,that is elements of this relation are
pairs of pairs of integers,such that ((a,b),(c,d)) ∈ R if and only if
a+d = b+c.Is R an equivalence relation?Explain.

先证递移性 {(a,b),(c,d)}∈ R {(c,d),(e,f)}∈ R=> a+d=b+c;c+f=d+e
=>a+d+c+f=b+c+d+e => a+f=b+e =>{(a,b),(e,f)}∈ R ...ok
再证对称性 {(a,b),(c,d)}∈ R =>a+d=b+c =>c+b=d+a =>{(c,d),(a,b)}∈ R
.OK
最后证反身行性{(a,b),(a,b)}∈ R => a+b=a+b 显然
=>R是等价关系

Let R be an arbitrary ring and （n属于Z+） .If the set Sn is def 英语翻译Let x,y,and z be positive integers such that y is a mult it is never party of it.that is one of the elements an idea The relation of genius to talent is the same as that of inst The relation of genius to talent is the same as that of isti Show that the relation R consisting of all pairs(x,y) such t Love is one of the two elements that the man values,the othe 5 elements of the environment that con't be influenced in th This is a 填什么 of the world .Let's put it up on the wall 英语翻译,time is one of the two elements that Americans save car 英语翻译求time is one of the two elements that amaricans save car time is one of the two elements that ameriacans save careful