Let `Z`be the setof all integers and `R`be therelation on `Z`defined a – InterviewSolution

InterviewSolution

1.	Let `Z`be the setof all integers and `R`be therelation on `Z`defined as `R={(a , b); a , b in Z ,`and `(a-b)`isdivisible by `5.}`. Prove that `R`is anequivalence relation.A. reflexiveB. reflexive but not symmetricC. symmetric and transitiveD. an equivalence relation
Answer» Correct Answer - D For reflexive : (a, a)=a-a=0 is divisible by 5. For symmetric : If (a-b) is divisible by 5, then b-a=-(a-b) is also divisible by 5. Thus relation is symmetric. For transitive If (a-b) and (b-c) is divisible by 5. Then (a-c) is also divisible by 5 Thus relation is transitive `therefore R` is an equivalence relation.

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