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Math Help - Relations Equivalence

  1. #1
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    Relations Equivalence

    I have a problem that asks about Equivalence of relations

    Here is the problem:

    a) Let R1 be the relation R1 = {(m,n) E Z X Z| |m| = |n|}. Show that R1 is an equivalence relation.


    and


    b) Find the equivalence classes of [0], [3], [-4] in R1

    Any help would be great.

    Thanks
    Tyson
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  2. #2
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    What have you done for yourself?
    Can you give it a start at least?
    Can you show the relation is reflexive?
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by tyelford View Post
    I have a problem that asks about Equivalence of relations

    Here is the problem:

    a) Let R1 be the relation R1 = {(m,n) E Z X Z| |m| = |n|}. Show that R1 is an equivalence relation.


    and


    b) Find the equivalence classes of [0], [3], [-4] in R1

    Any help would be great.

    Thanks
    Tyson

    Perhaps doing part (b) first would be helpful. For  n \in \mathbb{Z}, what elements are "related" to n?
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