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Math Help - Relation

  1. #1
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    Relation

    I am supposed to draw a diagram this is symmetric and antisymmetric, but is not the equality relation =.

    So far I can only come up with:

    1 <----> 2
    ^ ^
    l l
    l l
    v v
    3<----->4

    to show symmetry.

    Help please!
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  2. #2
    MHF Contributor

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    I am sorry to tell you that your posting is meaningless.
    What is the question in detail?
    What are you asking?
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  3. #3
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    The questions exactly is: Find a relatiom on the set [1,2,3,4] that is symmetric and antisymmetric, but is not the equality relation =.

    I was trying draw a picture to show symmetry which would be a double headed arrow between all elements. The diagram for antisymetric means that it is only a one head arrow. I need to try to find a way to do show both relations.
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  4. #4
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    Quote Originally Posted by undmath11 View Post
    The questions exactly is: Find a relatiom on the set [1,2,3,4] that is symmetric and antisymmetric, but is not the equality relation =.

    I was trying draw a picture to show symmetry which would be a double headed arrow between all elements. The diagram for antisymetric means that it is only a one head arrow. I need to try to find a way to do show both relations.
    What about the empty relation, call it R, on the set S = {1,2,3,4}?
    Since S is nonempty, convince yourself that R is irreflexive. This should tell you that R cannot be an equivalence relation.
    What now can be concluded about equality?
    Convince yourself that R is vacuously both symmetric and antisymmetric (and incidently, transitive).
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