
P(A)..Power set of A.
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 $\displaystyle P(X) \cup P(Y) \subset P(X \cup Y)$

What is the cardinality of A (denoted A)? The cardinality of P(A) is 2^A, so what you wrote is missing a few. Also, the elements of P(A) are subsets of A, so there's no way that 1 is an element of P(anything), since it's not a set.
I think once you get the first part straightened out, the second part won't give you much trouble.