## Thinking Mathematically (6th Edition)

$2^{n}$ - 1.
The number of distinct proper subsets of a set with n elements is $2^{n}$ - 1. we know that every subset except the set itself is a proper subset. In Table 2.4, we included the set itself when counting the number of subsets. If we want to find the number of proper subsets, we must exclude counting the given set, thereby decreasing the number by 1.