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Math Help - Hasse diagram: minimal, least, greatest

  1. #1
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    Hasse diagram: minimal, least, greatest

    Let S = {2,3,4,5} and consider the poset (S, <=) where <= is the divisibility relation. Which of the following is true?

    1. 3 is a minimal element
    2. 4 is a greatest element
    3. 2 is a least element
    4. Both 2 and 3

    My answer: 1

    In a Hasse diagram 3 and 5 are not connected to anything, and I'm unsure if this affects the answer. Suggestions?
    Last edited by nicnicman; December 18th 2012 at 06:13 AM.
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  2. #2
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    Re: Hasse diagram: minimal, least, greatest

    Quote Originally Posted by nicnicman View Post
    My answer: 1
    You are right. Other minimal elements are 2 and 5. Also, 3, 4 and 5 are maximal elements. There are no least or greatest elements.
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  3. #3
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    Re: Hasse diagram: minimal, least, greatest

    Yeah, that's what I thought. I just didn't know if there was some stipulation if the elements are not connected to other elements.

    Thank you.
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