True or false? Every natural and even number represents the cardinal of a set where two binary and closed operations are defined that give the whole the Boolean Algebra structure.
I know the following property of Boolean Algebras:
If $A$ is a finite Boolean Algebra, then its cardinal is $|A|=2^n$ for some $n\in\Bbb{N}$.
But I don't know if the statement has the form of implication or if it is simply: $$\forall n(p(n)),\quad p(n)=\text{Cardinal of a set where}\\\text{two binary and closed operations}\\\text{are defined that give the set the Boolean Algebra structure}.$$ Anyway, if I take $n=6$ it is even but there is no natural $n$ such that $2^n=6$.
Is the counterexample correct or how is it?