Question

In the set Z of integers, define mRn if m - n is divisible by 7. Prove that R is an equivalence
relation.​

Answer 1

Answer:

Then m – n is divisible by 7 and therefore n – m is divisible by 7. Thus, mRn ⇒ nRm and therefore R is symmetric. ... Thus, aRb and bRc ⇒ aRc and therefore R is transitive. Since R is reflexive, symmetric and transitive so, R is an equivalence relation on Z.