1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Hasse diagram: minimal, least, greatest
  1. Drawing Hasse Diagrams (Replies: 1)

Loading...