In the set Z of integers, define mRn if m - n is divisible by 7. Prove

1.	In the set Z of integers, define mRn if m - n is divisible by 7. Prove that R is an equivalencerelation.
Answer» 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.

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

Answer»

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.

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

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