Question

Determine and write the number of subsets in a set questions.Do the answers below

Answer 1

To determine the number of subsets of a set, you can use the formula \(2^n\), where \(n\) is the number of elements in the set. This is because each element can either be included in a subset or not, leading to \(2\) choices (include or exclude) for each of the \(n\) elements.

Here’s how you can determine the number of subsets for various examples:

1. **Empty Set**:
- Set: \(\{\}\)
- Number of elements (\(n\)): 0
- Number of subsets: \(2^0 = 1\)

2. **Set with 1 Element**:
- Set: \(\{a\}\)
- Number of elements (\(n\)): 1
- Number of subsets: \(2^1 = 2\) (subsets: \(\{\}, \{a\}\))

3. **Set with 2 Elements**:
- Set: \(\{a, b\}\)
- Number of elements (\(n\)): 2
- Number of subsets: \(2^2 = 4\) (subsets: \(\{\}, \{a\}, \{b\}, \{a, b\}\))

4. **Set with 3 Elements**:
- Set: \(\{a, b, c\}\)
- Number of elements (\(n\)): 3
- Number of subsets: \(2^3 = 8\) (subsets: \(\{\}, \{a\}, \{b\}, \{c\}, \{a, b\}, \{a, c\}, \{b, c\}, \{a, b, c\}\))

5. **Set with 4 Elements**:
- Set: \(\{a, b, c, d\}\)
- Number of elements (\(n\)): 4
- Number of subsets: \(2^4 = 16\)

You can apply the same reasoning to any set; simply find the number of elements and compute \(2^n\) for the number of subsets. If you have specific sets in mind, feel free to share, and I can help calculate!