# Binary relation

• May 3rd 2008, 11:29 AM
roger_darko
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?
• May 3rd 2008, 11:32 AM
Moo
Hello,

An equivalence relation is :

- symmetric : $aRb \Longrightarrow bRa$

- reflexive : $\forall a, \ aRa$

- transitive : $(aRb \text{ and } bRc) \Longrightarrow aRc$
• May 3rd 2008, 11:48 AM
roger_darko
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.
• May 3rd 2008, 11:58 AM
Plato
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.