Consider the following statements:

A. There exists a Boolean algebra with $5$ elements.

B. Every element of Boolean algebra has a unique complement.

C. If a Lattice $L$ is a Boolean algebra then $L$ is not relatively complemented.

D. The direct product of two Boolean Algebras is also a Boolean algebra.

Choose the correct answer about the four statements given above.

Statement A:

A finite Boolean algebra always has $2^n$ elements.

Possible number of elements can be:

$1,2,4,8,16,\ldots$

But $5$ is not of the form $2^n$.

So, statement A is false.

Statement B:

In Boolean algebra, every element has a unique complement.

So, statement B is true.

Statement C:

A Boolean algebra is complemented and distributive.

Also, every Boolean algebra is relatively complemented.

But statement C says it is not relatively complemented.

So, statement C is false.

Statement D:

The direct product of two Boolean algebras is also a Boolean algebra.

So, statement D is true.

Therefore, only B and D are correct.