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?

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- May 3rd 2008, 11:29 AMroger_darkoBinary 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 AMMoo
Hello,

An equivalence relation is :

- symmetric : $\displaystyle aRb \Longrightarrow bRa$

- reflexive : $\displaystyle \forall a, \ aRa$

- transitive : $\displaystyle (aRb \text{ and } bRc) \Longrightarrow aRc$ - May 3rd 2008, 11:48 AMroger_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 AMPlato
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.