Question Two - Partial Order

Consider the divisibility relation on the set 𝑆={2, 5, 7, 13 ,14, 70, 91, 182, 455} It is given that this relation is a partial order on 𝑆 (do not prove it!). a) Draw a Hasse diagram for this partial order b) Find all maximal elements and minimal elements The maximal elements are 70, 182, 455. The minimal elements are 2, 5, 7, 13. c) Does 𝑺 have a greatest element? Does 𝑺 have a least element? If so, write them down; if not, explain why not The greatest element is the element in the poset in which all other elements are partial orders of. The least element is the element in the poset which is a partial order of all other elements. There is no greatest element as 70≠182≠455, and these elements are not partial orders of each other. There is no least element as 2≠5≠7≠13, and these elements are not partial orders of each other. Untitled picture.png Machine generated alternative text: 455 oa 13

 

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