Finite boolean algebra can be embedded into $\mathcal P(n)$.

Question

I am trying to show that every finite boolean algebra can be embedded into $\mathcal P(n)$ for some large $n$. Any hints?

Answer 1

HINT: Let $B$ be a finite Boolean algebra. Let $A$ be the set of atoms of $B$. Show that every $b\in B$ is uniquely determined by $\{a\in A:a\le b\}$. What are the atoms of $\wp(n)$?