How to show that a relation is an equivalence relation given a defined relation

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Just apply the definition :

  • reflexivity : $a+a = 2 a$ is even, so $aRa$

  • symetric : if $aRb$ then a+b is even, then b+a is even then $bRa$

  • transitive : if $aRb$ and $bRc$ then a+b is even and b+c is even, then a+2b+c is even then a+c is even (because 2b is even), then $aRc$

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Jared
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Jared

Updated on August 01, 2022

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  • Jared
    Jared over 1 year

    I understand for the most part the conceptual aspects of an equivalence relation. A relation is considered a equivalence relation if it satisfies reflexive, symmetric and transitive properties but Im having trouble working with this on paper.

    For example, Given a relation R defined on the integers by aRb <=> a+b is even, show that this relation is an equivalence relation.

    So far my approach is. Reflexive, aRa <=> a+a is even Symmetric, if bRa <=> b+a is even Transitive, if aRb and bRc then aRc <=>a+c is even.

    But after that i am stuck.