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Math Help - Partial Order relation and hasse diagram mxa/min

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    69

    Partial Order relation and hasse diagram mxa/min

    I have a set
    A={2,3,4,5,12,15,18} with a x|y relationship.
    Therefore, I beleive,
    R = {
    (2,2) (2,4) (2,12) (2,18)
    (3,3) (3,12) (3,15) (3,18)
    (4,4) (4,12)
    (5,5) (5,15)
    (12,12)
    (15,15)
    (18,18)
    }

    I can prove a partial order relationship with a directed graph showing reflexive, transistive and antisymetric.

    Does the hasse diagram look like this?
    Partial Order relation and hasse diagram mxa/min-photo-0205.jpg
    max = 18
    min = 2,5

    18 is the greatest,
    There is no and least vertex because more than 1 minimal.

    is this correct?
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  2. #2
    Junior Member
    Joined
    Oct 2006
    Posts
    71
    Quote Originally Posted by dunsta View Post
    I have a set
    A={2,3,4,5,12,15,18} with a x|y relationship.
    Therefore, I beleive,
    R = {
    (2,2) (2,4) (2,12) (2,18)
    (3,3) (3,12) (3,15) (3,18)
    (4,4) (4,12)
    (5,5) (5,15)
    (12,12)
    (15,15)
    (18,18)
    }

    I can prove a partial order relationship with a directed graph showing reflexive, transistive and antisymetric.

    Does the hasse diagram look like this?
    Click image for larger version. 

Name:	Photo-0205.jpg 
Views:	63 
Size:	16.4 KB 
ID:	19084
    max = 18
    min = 2,5

    18 is the greatest,
    There is no and least vertex because more than 1 minimal.

    is this correct?
    You might want to review the definitions of least element and greatest element
    (as they're defined in the given context).

    With respect to A, 12, 15 and 18 look maximal to me. There is no greatest.
    And 2, 3 and 5 look minimal to me. There is no least.

    As convincing as it might be, a poset diagram (or any other drawing for that matter) doesn't really
    "prove" anything. Of course, that's just my narrow-minded opinion.
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