Prove that the relation R in the set A={5,6,7,8,9} given by R={(a,b):mode of a-b is divisible by 2},is an equivalence function .Find all elements related to 6

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We haveA=5,6,7,8,9aRb: a-b is divisible by 2...iReflexiveaRa: a-a=0 which is divisible by 2.Hence R is reflexive.SymmetricbRa:b-a=-a-b=a-b which is divisible by 2 by iHence R is symmetric.Transitive:a-b is divisible by 2andb-c is divisible by 2Hence sumation of value inside mod will also be divisible by 2.a-b+b-c  is divisible by 2a-c  is divisible by 2Hence R is transitive .R is reflexive, symmetric and transitive, hence it is equivalence relation.Elements related to 6 are 6,8,8,6

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