Hey all,

Given $\displaystyle A = \{\emptyset, 1, \{2,3\}\}$

Is

$\displaystyle P(A) = \{\emptyset, 1, \{1,\{2,3\}\},\{2,3\}\}$ ?

And also how can I prove that for all sets $\displaystyle X$ and $\displaystyle Y$ we have $\displaystyle P(X) \cup P(Y) \subset P(X \cup Y)$