1. **Problem Statement:** List all subsets for the given sets and find the number of subsets for each. 2. **Recall the formula for number of subsets:** For a set with $n$ elements, the number of subsets is given by: $$2^n$$ This includes the empty set and the set itself. 3. **Set ①: $\{0, 5\}$** - Number of elements $n=2$ - Number of subsets $= 2^2 = 4$ - Subsets are: - $\emptyset$ - $\{0\}$ - $\{5\}$ - $\{0, 5\}$ 4. **Set ②: $\{x \mid x \text{ is a prime number } \leq 10\}$** - Prime numbers less than or equal to 10 are $2, 3, 5, 7$ - Number of elements $n=4$ - Number of subsets $= 2^4 = 16$ - Subsets include: - $\emptyset$ - $\{2\}$, $\{3\}$, $\{5\}$, $\{7\}$ - $\{2, 3\}$, $\{2, 5\}$, $\{2, 7\}$, $\{3, 5\}$, $\{3, 7\}$, $\{5, 7\}$ - $\{2, 3, 5\}$, $\{2, 3, 7\}$, $\{2, 5, 7\}$, $\{3, 5, 7\}$ - $\{2, 3, 5, 7\}$ **Final answers:** - Number of subsets for $\{0, 5\}$ is $4$ - Number of subsets for $\{2, 3, 5, 7\}$ is $16$