4 votes 4 votes Why is it not lattice? Set Theory & Algebra set-theory&algebra lattice + – Pradip Nichite asked Dec 19, 2015 Pradip Nichite 1.2k views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply Umang Raman commented Dec 19, 2015 reply Follow Share its a lattice. Lattice : A poset (L , ≤) is a Lattice iff for all a , b ∈ L LUB(a,b) and GLB(a,b) both exist and ∊ L 1 votes 1 votes Pradip Nichite commented Dec 19, 2015 reply Follow Share In made easy test series they have said it is not a lattice. 0 votes 0 votes Umang Raman commented Dec 19, 2015 reply Follow Share reason? 0 votes 0 votes Pradip Nichite commented Dec 20, 2015 reply Follow Share No reason has given. 0 votes 0 votes Please log in or register to add a comment.
Best answer 10 votes 10 votes A lattice must be first a poset i.e. it should be reflexive , anti-symmetric and transitive. Here b ≤ c & c ≤ b so, it is not antisymmetric & hence not a lattice. Himanshu1 answered Dec 20, 2015 selected Jan 13, 2016 by Himanshu1 Himanshu1 comment Share Follow See 1 comment See all 1 1 comment reply Pradip Nichite commented Dec 20, 2015 reply Follow Share Thank you 1 votes 1 votes Please log in or register to add a comment.