Determine the number of subsets contained in S if S = x is an even, positive integer and x < 23 .

Question

Determine the number of subsets contained in S if S = x .

Answer 1

The even, positive integers less than 23 make up the set S with 11 elements, and by using the formula 2^n, we find that S has 2048 subsets.

Step-by-step explanation:

To determine the number of subsets contained in the set S given that S = x is an even, positive integer and x < 23 , we first need to establish the elements of set S. Since the set consists of even numbers less than 23, the elements of set S are {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}. There are 11 elements in the set. The formula to find the number of subsets for a set with n elements is 2^n. Therefore, the number of subsets of set S is 2^11, which equals 2048.

Step-by-Step Explanation

1. List all the even, positive integers less than 23.
2. Count the number of elements in the set, which is 11.
3. Use the formula 2^n, where n is the number of elements, to find the number of subsets.
4. Calculate 2^11 to get the number of subsets.

This means that the set S has 2048 different subsets, including the empty set and the set itself.