# Discrete Math- Equivalence Relations

Please help with the following problem regarding discrete math.

I need a clear explanation of what an equivalence relation is with an examples. Specifically given 5|(m-n), where m and n are integers, please verify if this is an equivalence relation.

Please explain this clearly and in detail.

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#### Solution Preview

Problem: I need a clear explanation of what an equivalence relation is with an examples. Specifically given 5|(m-n), where m and n are integers, please verify if this is an equivalence relation.

Solution:

I hope the following answer is clear. Thanks.

Solution:

First of all, I would like to give a definition of "equivalence relation":

A given binary relation ~ on a set A is said to be an equivalence relation if, and only if, it is reflexive, symmetric and transitive. Equivalently, for all a, b and c in A:

? a ~ a. (Reflexivity)

? if a ~ b then b ~ a. ...

#### Solution Summary

This solution helps with a problem regarding discrete math equivalence relations. Step by step calculations are given for each problem.