Solution
= Solution
A <subset> is determined uniquely by deciding, for each of the $n$ elements, whether to include it. Each decision has two possibilities. By the <rule of product>, there are $2\cdot2\cdots2=2^n$ decision strings. The correspondence between such binary strings and <subsets> is a <bijection>, so \b[$|\mathcal P(\mathcal U)|=2^n$]. The all-zero string corresponds to the empty <subset>.