The problem asks for the formula that represents the cardinality (number of elements) of the power set of a set with $n$ elements.

1. Problem Description

The problem asks for the formula that represents the cardinality (number of elements) of the power set of a set with $n$ elements.

2. Solution Steps

The power set of a set $S$ is the set of all subsets of $S$, including the empty set and $S$ itself. If a set $S$ has $n$ elements, the number of subsets of $S$ is $2^n$. This is because for each element in $S$, there are two possibilities: either the element is in the subset, or it is not. Since there are $n$ elements, there are $2 \times 2 \times \dots \times 2$ ($n$ times) possible subsets, which is $2^n$.

The cardinality of the power set of a set with $n$ elements is $2^n$.

3. Final Answer

e. $2^n$