Question

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

Answer 1

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