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Math Help - Binary relation

  1. #1
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    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?
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  2. #2
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    Hello,

    An equivalence relation is :

    - symmetric : aRb \Longrightarrow bRa

    - reflexive : \forall a, \ aRa

    - transitive : (aRb \text{ and } bRc) \Longrightarrow aRc
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  3. #3
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    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.
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  4. #4
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    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.
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