Let $\displaystyle A$ and $\displaystyle B$ be nonempty sets such that $\displaystyle |A| < |B|$. Show there exists an injective function from $\displaystyle \mathcal{P}(A)$ to $\displaystyle \mathcal{P}(B)$.

This was a question on my final and luckily I was able to omit it because I wasn't sure how to tackle this problem, but I'm curious to what the answer is. Thanks!