Define a relation on the set of integers by a R b a-b is divisible by 5

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Define a relation RR on the set of integers Z\mathbb Z by a R b  ⟺  a−b is divisible by 5.a \thinspace R \thinspace b \iff a-b \text{ is divisible by }5. Prove, with reasons, whether RR is reflexive, symmetric and transitive. Conclude whether RR is an equivalence relation.

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