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Homework Help: Hasse diagram: minimal, least, greatest

  1. Dec 18, 2012 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations

    3. The attempt at a solution
    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: Dec 18, 2012
  2. jcsd
  3. Dec 18, 2012 #2


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    Science Advisor
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    Gold Member

    I agree with your answer. The presence of an element that has no ordering relation with any other means there cannot be a greatest or a least.
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