Let n be a fixed positive integer. Define a relation R on the set Z of integers by thenR isa)reflexiveb)symmetricc)transitived)equivalenceCorrect answer is option 'A,B,C,D'. Can you explain this answer?

Question

Let n be a fixed positive integer. Define a relation R on the set Z of integers by  thenR isa)reflexiveb)symmetricc)transitived)equivalenceCorrect answer is option 'A,B,C,D'. Can you explain this answer?

Answer

D. if aRa implies n always divides a-a for all a so it is reflexive again if we let aRb so n/a-b so n will divide -(a-b) which implies bRa so it is symmetric again if aRb and bRc = n/ a- b and n/ b-c so n / (a-b) +(b-c) which is equal to n/ a-c so we will get if arb and bRc then aRc so it is transitive since this relation satisfy all the conditions of equivalence relation so it is an equivalence relation

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