Subset Math Example 2

Solution

1. 1
   A set with $n$ elements has exactly $2^n$ subsets (including $\emptyset$ and the set itself). Here $|S| = 3$, so there are $2^3 = 8$ subsets.
2. 2
   List subsets by size systematically — size 0: $\emptyset$. Size 1: $\{a\}, \{b\}, \{c\}$. Size 2: $\{a,b\}, \{a,c\}, \{b,c\}$. Size 3: $\{a,b,c\}$.
3. 3
   Verify the count: $1 + 3 + 3 + 1 = 8 = 2^3$ ✓. These 8 sets form the power set $\mathcal{P}(S)$.