Counting Subsets

How many subsets does a set with $n$ elements have? For each element, you have 2 choices: include it or exclude it. By the product rule, the total is $2 \times 2 \times ... \times 2 = 2^n$.

For $\{a, b, c\}$, the 8 subsets are: $\{\}, \{a\}, \{b\}, \{c\}, \{a,b\}, \{a,c\}, \{b,c\}, \{a,b,c\}$. This includes the empty set and the full set.