For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets. \( \{18,15,13,17,12\} \) The number of subsets is The number of proper subsets is

To calculate the number of subsets for a set, we can use the formula: \[ \text{Number of subsets} = 2^n \] where \( n \) is the number of elements in the set. In the given set \( \{18, 15, 13, 17, 12\} \), there are 5 elements. Therefore, we have: \[ n = 5 \] Calculating the number of subsets: \[ \text{Number of subsets} = 2^5 = 32 \] Next, to find the number of proper subsets, we use the fact that the number of proper subsets is equal to the total number of subsets minus 1 (to exclude the set itself): \[ \text{Number of proper subsets} = \text{Number of subsets} - 1 = 32 - 1 = 31 \] Thus, the results are: - The number of subsets is \( 32 \). - The number of proper subsets is \( 31 \).