set theory

Question

Which of the following statements about the POSET diagram given below is TRUE ?

For a lattice with 8 elements to be called as boolean algebra 

A) It is a necessary and a sufficient condition that it should be isomorphic to above POSET diagram.

B) It is necessary condition  to be isomorphic to above POSET diagram but not a sufficient condition. 

C) It is sufficient condition but not a necessary condition.

Which among A),B),C) is true ..? why ? please explain ?

Answer 1

There are two necessary and sufficient conditions for a POSET to be boolean algebra :

1. Number of elements should be 2^n.

2.Number of edges should be n*2^(n-1).

In given diagram,these both conditions are true and only those who are isomorphic to this graph will be boolean algebra.

Option A is correct