1. **Problem 1: List all subsets of the set {0, 5} and find the number of subsets.** - The set is $\{0, 5\}$ which has 2 elements. - The formula for the number of subsets of a set with $n$ elements is $2^n$. - Here, $n=2$, so the number of subsets is $2^2 = 4$. - The subsets are: 1. $\emptyset$ (the empty set) 2. $\{0\}$ 3. $\{5\}$ 4. $\{0, 5\}$ 2. **Problem 2: List all subsets of the set of prime numbers less than or equal to 10 and find the number of subsets.** - The prime numbers less than or equal to 10 are $\{2, 3, 5, 7\}$. - The set has 4 elements. - Using the formula $2^n$, the number of subsets is $2^4 = 16$. - The subsets include: 1. $\emptyset$ 2. $\{2\}$ 3. $\{3\}$ 4. $\{5\}$ 5. $\{7\}$ 6. $\{2, 3\}$ 7. $\{2, 5\}$ 8. $\{2, 7\}$ 9. $\{3, 5\}$ 10. $\{3, 7\}$ 11. $\{5, 7\}$ 12. $\{2, 3, 5\}$ 13. $\{2, 3, 7\}$ 14. $\{2, 5, 7\}$ 15. $\{3, 5, 7\}$ 16. $\{2, 3, 5, 7\}$ **Summary:** - Number of subsets for $\{0, 5\}$ is $4$. - Number of subsets for $\{2, 3, 5, 7\}$ is $16$. This uses the fundamental rule that a set with $n$ elements has $2^n$ subsets, including the empty set and the set itself.