Question related to Boolean Algebra.

Question

I am asked to prove that order of a Boolean Algebra cannot be prime greater than 2. I have a dificulty to show this in an appriopriate way. I know the definition of Boolean Algebra. The definition I have seen is as follows: A structure (B,meet,join) is called a Boolean Algebra if B is distributive, a join 1 = 1, a meet 0 = 0 , a join a' = 1, a meet a' = 0. Any help will be appreciated.

Answer 1

Hint

See Boolean algebra (structure) :

It can be shown that every finite Boolean algebra is isomorphic to the Boolean algebra of all subsets of a finite set. Therefore, the number of elements of every finite Boolean algebra is a power of two.

See also Stone representation.