Partial Order on X: Maximal, Minimal, Greatest & Least Elements

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SUMMARY

The discussion revolves around defining a partial order on the set X = {2, 3, 4, 5, 8, 9, 15, 27, 45} based on divisibility. The maximal elements are {27, 45}, while the minimal element is 2. There is no greatest element since not all elements in X can be divided by a single element, and the least element is 2. Additionally, participants are encouraged to draw the Hasse diagram to visualize the relationships within the set.

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PeterWatson
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I'm stumbling on this basic question!

Let X = {2,3,4,5,8,9,15,27,45}.
Define a partial order | on X such that x|y <--> x divides y.

(a) Find the maximal and minimal elements
(b) Is there a greatest element, if so what is it?
(c) Is there a least element, if so what is it?
(d) Draw the Hasse diagram

Please help!
 
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Hi Peter! Welcome to PF! :wink:

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