Let $A = \{1,2,3,\ldots,9\}\text{.}$
1. How many subsets of $A$ are there? That is, find $|\pow(A)|\text{.}$ Explain.
2. How many subsets of $A$ contain exactly 5 elements? Explain.
3. How many subsets of $A$ contain only even numbers? Explain.
4. How many subsets of $A$ contain an even number of elements? Explain.