48. How many subsets does an $n$-element set have?
48. Let there be a set with $n$ elements. For each element, there are two possibilities: to be included in a subset or not to be included. Then for all $n$ elements, we get $\underbrace{2 \cdot 2 \cdot 2 \ldots 2}_{n}=$ $=2^{n}$ such possibilities, i.e., $2^{n}$ different subsets.