Partial Order relation and hasse diagram mxa/min

• Sep 27th 2010, 09:28 PM
dunsta
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?
Attachment 19084
max = 18
min = 2,5

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

is this correct?
• Sep 27th 2010, 11:02 PM
PiperAlpha167
Quote:

Originally Posted by dunsta
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?
Attachment 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.