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Math Help - how Z (integer) is an equivalence relation.

  1. #1
    rcs
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    how Z (integer) is an equivalence relation.

    Prove that the relation on Z (integer) define by a~b iff a b is divisible by 5. is an equivalence relation.

    Can anybody help me on this
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: how Z (integer) is an equivalence relation.

    Quote Originally Posted by rcs View Post
    Prove that the relation on Z (integer) define by a~b iff a b is divisible by 5. is an equivalence relation.

    Can anybody help me on this
    Prove that ~ is reflexive relation, symmetric and transitive.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: how Z (integer) is an equivalence relation.

    Another little help:

    Reflexive: For all a\in\mathbb{Z} we have

    a-a=0=5\cdot 0 that is, a-a is divisible by 5 which means that a\sim a

    Try the rest.
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