0 0 votes Consider the following POSETs: Which of the above POSETs are isomorphic to (P (S), ⊆), where S = {a, b, c}? Set Theory & Algebra engineering-mathematics + – balchandar reddy san 740 views answer comment Share Follow Print See all 3 Comments 3 3 Comments reply Shaik Masthan commented Jan 30, 2019 i edited by Shaik Masthan Jan 31, 2019 reply Follow flag first type the question instead of screenshot ! Coming to the question :- points about (P (S), ⊆) :- i) contains number of elements in power of 2, eliminate II ii) it is not totally ordered ! ===> eliminate I iii) every element should have unique complement ! Simply saying :- after matching with i) and ii) condition, draw the hasse diagram and draw the hasse diagram with set S = {1,2,....n} then those two hasse diagrams are equal if you remove labels 0 0 replyShare newdreamz a1-z0 commented Jan 31, 2019 reply Follow flag @Shaik Masthan i doubt sir why the III is not isomorphic to (P (S), ⊆) as per convention (P (S), ⊆) with A={a,b,c} is a boolean algebra with 2^n =2^3=8 elements and having a cubic shape lattice also we know poset [Dn,\] is also a a boolean algebra with the condition that Dn should not have any square factors and number of elements in Dn should be 2^n. Also any boolean algebra with number of elements 8 should be isomorphic to (P (S), ⊆) where S having 3 elements. 1 1 replyShare Shaik Masthan commented Jan 31, 2019 reply Follow flag ya it's my fault to eliminate III ! 0 0 replyShare Please log in or register to add a comment.
