Proof on not subset of one and other?

Question

Let $A = \{ 2^n -1 |$ n is a prime integer } and let $B$ be the set of all prime integers. Show that $A \not\subset B$ and $B \not\subset A$.

Answer 1

To show that $B\not\subset A$ a counter example is $5$ since $5\in B$ but $5\not\in A$.

To show that $A\not\subset B$ a counter example is $2^{11}-1$ since $2^{11}-1\in A$ but $2^{11}-1\not\in B$ since we have $2^{11}-1=23\times89$.