1. **State the problem:** We need to find the number of subsets and the number of proper subsets of the set $\{29, 5, 14, 9\}$. 2. **Recall the formula:** For a set with $n$ elements, the number of subsets is given by: $$ 2^n $$ This is because each element can either be included or excluded from a subset. 3. **Number of subsets:** The set has 4 elements, so: $$ 2^4 = 16 $$ Therefore, the number of subsets is 16. 4. **Number of proper subsets:** Proper subsets are all subsets except the set itself. So, the number of proper subsets is: $$ 2^n - 1 $$ For our set: $$ 2^4 - 1 = 16 - 1 = 15 $$ 5. **Final answers:** - Number of subsets: 16 - Number of proper subsets: 15