Questions: For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets 8,15,9,6,17 The number of subsets is .

Solution Steps

To solve the problem of finding the number of subsets and proper subsets for a given set, we can use the following approach:

1. Number of Subsets: For a set with \( n \) elements, the number of subsets is \( 2^n \). This includes all possible combinations of the elements, including the empty set and the set itself.

2. Number of Proper Subsets: Proper subsets are all the subsets excluding the set itself. Therefore, the number of proper subsets is \( 2^n - 1 \).

Given the set \(\{8, 15, 9, 6, 17\}\), we first determine the number of elements in the set, then apply the formulas above to find the number of subsets and proper subsets.

The given set is \( \{8, 15, 9, 6, 17\} \). The number of elements in this set is \( n = 5 \).

The formula for the number of subsets of a set with \( n \) elements is given by: \[ \text{Number of Subsets} = 2^n \] Substituting \( n = 5 \): \[ \text{Number of Subsets} = 2^5 = 32 \]

The number of proper subsets is calculated by excluding the set itself from the total number of subsets: \[ \text{Number of Proper Subsets} = 2^n - 1 \] Substituting \( n = 5 \): \[ \text{Number of Proper Subsets} = 2^5 - 1 = 32 - 1 = 31 \]

Final Answer