ME FLT5

Question

 

Consider the following POSETs:

 

Which of the above POSETs are isomorphic to (P (S), ⊆), where S = {a, b, c}?

Comments

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

---

@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.

 

---

ya it's my fault to eliminate III !