Originally Posted by

**amthomasjr** Hey guys, I wanted to see if someone could check my work.

Find $\displaystyle \mathcal{P}(\mathcal{P}(\left\{1\right\}))$ and its cardinality.

$\displaystyle \mathcal{P}(\left\{1\right\})=\left\{\oslash, \left\{1 \right\}\right\}$ then,

$\displaystyle \mathcal{P}(\mathcal{P}(\left\{1\right\}))= \mathcal{P}(\left\{\oslash, \left\{1 \right\}\right\}) = \left\{\oslash, \left\{1 \right\}, \left\{\left\{1 \right\}\right\}, \left\{\oslash, \left\{1 \right\}\right\}\right\}$

$\displaystyle | \mathcal{P}(\mathcal{P}(\left\{1\right\}))| = 4$ correct?