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**Nivagator** Hello, noob on here. Having trouble proving an equivalence relation...

Given:

Define a relation R on $\displaystyle Z$ (the integers) by $\displaystyle nRm$ if $\displaystyle m - n$ is a multiple of 5.

a. Show that R is an equivalence Relation

b. How many equivalence classes are there for R?

a. I know that in order to prove an equivalence relation, you must show that a relation is reflexive, symmetric and transitive.

Reflexive, nRn

Let x be an element of n

$\displaystyle x-x=0$

0 is a multiple of 5

therefore, nRn

therefore, R is reflexive.

I have no idea how to go about proving Symmetric and Transitive without using actual numerical values.

b. I do not know how to determine the number of equivalence classes exist for R.

Thanks in advance, sorry I don't have more to offer.

Gavin