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Math Help - Lattice - partial order

  1. #1
    Mel
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    Lattice - partial order

    Conside the poset ({2,4,6,7, 9, 12, 18, 27, 36, 48, 60, 72}, |), with the indicated integers and the divides relation. Find the following if they exist; if they do not exist explain why.

    a.) maximal and minimal elements
    b.) greatest and least elements
    c.) least upper bound of {2, 12}
    d.) greatest lower bound of {60; 72}
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  2. #2
    MHF Contributor

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    Did you graph the poset? If you understand the definitions, then using a graph makes it easy.
    Attached Thumbnails Attached Thumbnails Lattice - partial order-poset2.gif  
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  3. #3
    Mel
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    Thanks. That really helped.
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  4. #4
    Mel
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    Plato - more help

    If we change the order of the poset to ({2, 4, 9, 6, 18, 12, 36, 27, 72, 60, 48 is it compatible with the partial ordering of the divides relation mentioned above?
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