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Math Help - Poset troubles

  1. #1
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    Poset troubles

    Hello ppl :-)

    A={3,5,9,15,24,45} . Also R={(x,y) | x divides y} . Proove that
    1) R is partial ordered

    2) Hasse diagramm for R

    3) Upper bounds of {3,5} , Lower bounds for {15,45}

    -------

    for 1) i have to show that R is reflexive, antisymmetric, and transitive

    not sure how to show it for this particular problem though.


    2) xy
    / \
    x y
    \ /
    0


    3) No idea =/
    Last edited by primeimplicant; September 5th 2010 at 02:36 AM.
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  2. #2
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    for 1) i have to show that R is reflexive, antisymmetric, and transitive

    not sure how to show it for this particular problem though.
    Start by writing the definition: what it means for R to be reflexive. Substitute the definition of R into that expression.

    2) xy
    / \
    x y
    \ /
    0
    A Hasse diagram is a graph where vertices are elements of the partially ordered set, i.e., A. Zero is not a member of A and neither are x and y.

    3) Upper bounds of {3,5} , Lower bounds for {15,45}
    Again, write the definition, what it means for a number x to be an upper bound of 3 and 5 and substitute the definition of R there.
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