Equivalence relation - Congruence modulo

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What have you tried so far? You should prove by definition that the given relation is reflexive, symmetric and transitive. Can you do that?

Thank you. I am familiar with the properties reflexive, symmetric and transitive, but not when it comes to modulo. I have never seen it before, and simply do not know where to start.

The relation is defined as
To check if the relation is reflexive you have to check which is true because .

Can you check the symmetric and transitive property now?

Quote:

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Originally Posted by aprilrocks92

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I have a different but equidistant way of describing that relation.
Say if and only if have the same remainder when divided by

Thus it should be clear that .

The three needed properties are easily checked.

There are five equivalence classes.