3 votes 3 votes Set Theory & Algebra set-theory&algebra lattice + – richa116 asked Jan 5, 2016 • recategorized Jul 18, 2016 by LeenSharma richa116 833 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
4 votes 4 votes Option a As complement m∨n=1 and m∧n=0 m∨p=1 and m∧p=0 So both n and p are complements of m For distirbutive lattice N∧(m∨p)= (N∧m)∨(N∧p) From lhs. n∧(m∨p)=n∧1=n From rhs. n∧m=0 n∧p=p And 0∨p= p So lhs≠ rhs that's why given lattice is non-distributive khushtak answered Jan 5, 2016 • edited Jan 5, 2016 by khushtak khushtak comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Answer will be (A) S1: is true because complement of a lattice and lattice has a lub and a glb S2: Distributive lattice each element has atmost one complement. but here m has 2 complement srestha answered Jan 5, 2016 srestha comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes S1: for lattice to be complemented there should exist LUB and GLB for pair of elements eg :(m,n) its LUB is 1 and its GLB is 0 S2: for a lattice to be distributive complement should be unique in above diagram we have two complements of m that is n,p so it is not distributive lattice so (A) option focus _GATE answered Jan 5, 2016 focus _GATE comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes By above diagram you can see that complement of m is n and p. Since there exist an vertex m such that it have more than on complement so it voilet the deffinition of distributive lattice. Paras Nath answered Sep 21, 2016 Paras Nath comment Share Follow See all 0 reply Please log in or register to add a comment.