4 votes 4 votes Which of the following statements are true? Every totally ordered set is a lattice Every lattice has a least element and a greatest element All totally ordered posets are also well ordered posets. i only ii and iiii only ii only i, ii and iii Set Theory & Algebra tbb-mockgate-2 discrete-mathematics set-theory&algebra lattice + – Bikram asked Jan 24, 2017 • edited Sep 12, 2020 by ajaysoni1924 Bikram 821 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 5 votes 5 votes Only bounded lattice has a least and a greatest element. All well-ordered sets are also totally ordered sets, but not vice- versa . Bikram answered Jan 24, 2017 • edited Dec 15, 2018 by Arjun Bikram comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Arjun commented Dec 15, 2018 reply Follow Share No, the wiki link says that for a well ordered set, the following 4 points are equivalent (implies each other). It is not saying that a total order is a well order. 0 votes 0 votes HeadShot commented Jan 13, 2019 reply Follow Share total order = each element must be related to every other element. well order : least element must be present. @pps121 now analyse and if still not getting then i ll suggest K.H.Rosen , its beautiful explained there. 1 votes 1 votes Abhisek Tiwari 4 commented Jan 19, 2019 reply Follow Share @HeadShot well ord: lattice + least element? or poset? 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Correct Option A Every totally ordered set is a lattice. Becasue in TOSET every element is comparable to every other element. SO, LUB(a,b) and GLB(a,b) for each pair a,b will exist. Only this statement is correct. aaaakash001 answered Nov 7, 2022 aaaakash001 comment Share Follow See all 0 reply Please log in or register to add a comment.
