Question

In Z, the set of all integers,the relation R defined by '(x,y)€ R imples 5 divides x-y' then show that R is an equvilence relation
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Answer 1

ANSWER

R={(x,y):x,y∈z,x−yisdivisiblebyn}ForReflexive,x∈zSo⇒(x−x)isdivisiblebyn⇒(x,x)∈z

So, Relation is Reflexive

ForSymmetric⇒Let(x,y)∈R⇒(x−y)isdivisiblebyn.⇒nx−y=c,Remainderis0.⇒ny−x=−c,Remainderisalso0.⇒(y−x)isdivisibl