Question

We define a relation R on the set Z of integers by
nRm if n^2 - m^2 is divisible by 5:
1. Prove that R is an equivalence relation.
2. Describe the equivalence classes.

Answer 1

An equivalence relation is a relation that meets all the following three criteria:

1. xRx
2. If xRy then yRx
3. If xRy and yRz, then xRz

Answer 2

For example, in this case, nRn if n^2-n^2=0 is divisible by 5, which is true. Do this for the other two relations.

Answer 3

thanks!