Thread: Binary relation

Given the binary relation R on N define by aRb iff | a -b | is even.

How can I verify that R is an equivalence relation?

Hello,

An equivalence relation is :

- symmetric :

- reflexive :

- transitive :

I understand that part, just a bit confused on how to use |x - y| to prove all these three steps. I noticed ix and y have to both be either odd or even to satisfy the iff statement. I just need a starting point with the problem, any help would be appreciated.

Is it true that |a-b|=|b-a|?

Is it true that zreo is an even number?

There are two BIG hints for the first two.