Find the number of subsets that can be formed from the set `A={4,5,6}`

Answer

To find the number of subsets that can be formed from the set \( A = \{4, 5, 6\} \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Set and Its Elements**:
The given set \( A \) contains three elements: 4, 5, and 6.

2. **Determine the Number of Elements (n)**:
Count the number of elements in set \( A \). Here, \( n = 3 \).

3. **Use the Subset Formula**:
The formula to calculate the number of subsets of a set is given by \( 2^n \), where \( n \) is the number of elements in the set.

4. **Calculate the Number of Subsets**:
Substitute the value of \( n \) into the formula:
\[ 2^n = 2^3 = 8 \]
Therefore, the total number of subsets is 8.

5. **List the Subsets**:
To verify, we can list all the subsets:
- The empty set: \( \{\} \)
- Single-element subsets: \( \{4\}, \{5\}, \{6\} \)
- Two-element subsets: \( \{4, 5\}, \{4, 6\}, \{5, 6\} \)
- The full set: \( \{4, 5, 6\} \)

Listing them out, we have:
1. \( \{\} \)
2. \( \{4\} \)
3. \( \{5\} \)
4. \( \{6\} \)
5. \( \{4, 5\} \)
6. \( \{4, 6\} \)
7. \( \{5, 6\} \)
8. \( \{4, 5, 6\} \)

6. **Conclusion**:
Thus, the total number of subsets that can be formed from the set \( A = \{4, 5, 6\} \) is **8**.