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Math Help - sets and relations #2

  1. #1
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    sets and relations #2

    Let A={1,2,4,6,8} and for a ,b, Element of A, define a < b if and only if b/a is an integer.
    (a) prove that < defines a partial order on A
    (b) draw the Hasse diagram for <
    (c) List all minimum, minimal, maximum, and maximal elements.
    (d) Is (A, <) totally ordered? explain
    Last edited by mr fantastic; March 18th 2011 at 06:43 PM. Reason: Title.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tygracen View Post
    Let A={1,2,4,6,8} and for a ,b, Element of A, define a < b if and only if b/a is an integer.
    (a) prove that < defines a partial order on A
    what does the definition of "partial order" say?

    you have to show that reflexivity, antisymmetry and transitivity holds

    see: Partial Order -- from Wolfram MathWorld

    (b) draw the Hasse diagram for <
    see here

    (c) List all minimum, minimal, maximum, and maximal elements.
    again, what you need to do here becomes clear when you write out the definitions, which i won't do since that's reinventing the wheel. check your text, or google, or wikipedia, or ....

    (d) Is (A, <) totally ordered? explain
    in addition to being a partial order, can any two elements be compared?

    see: Totally Ordered Set -- from Wolfram MathWorld
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