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Math Help - Relations

  1. #1
    Junior Member
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    Relations

    Hi, Im determining which relations are reflexsive, transitive, summetric or antisymmetric on set A = {x,y,z}.

    Ive come up with following:

    1) {(x,y), (y,x)} = symmetric
    2) {(x,x), (y,y)} = reflexsive
    3) {(x,x) , (y,y), (z,z), (x,z)} = reflexsive
    4) A^2 = reflexsive, symmetric, transitive
    5) 0 (empty set) = neither (im not sure on this one)
    6) {(x,y), (x,x), (x,z)} = reflexsive

    Can somebody please check my answers and provide some help where i have goone wrong? Many thanks.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by kurac View Post
    Hi, Im determining which relations are reflexsive, transitive, summetric or antisymmetric on set A = {x,y,z}.

    Ive come up with following:

    1) {(x,y), (y,x)} = symmetric
    correct!


    2) {(x,x), (y,y)} = reflexsive
    incorrect! the correct answer is "neither". note that (z,z) is not in the set. so it's not reflexive.


    3) {(x,x) , (y,y), (z,z), (x,z)} = reflexsive
    incorrect! reflexive and transitive.


    4) A^2 = reflexsive, symmetric, transitive
    correct!


    5) 0 (empty set) = neither (im not sure on this one)
    incorrect! symmetric and transitive but not reflexive.


    6) {(x,y), (x,x), (x,z)} = reflexsive
    incorrect! transitive.
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