If a set has 2 elements then the difference between the subsets of its powers set and numbers of its subset is

Options

A. 2
B. 8
C. 10
D. 12

Answer

To solve the problem, we need to find the difference between the number of subsets of the power set of a set \( A \) with 2 elements and the number of subsets of the set \( A \).

### Step-by-Step Solution:

1. **Identify the number of elements in set \( A \)**:
- Given that set \( A \) has 2 elements.

2. **Calculate the number of subsets of set \( A \)**:
- The formula to find the number of subsets of a set with \( n \) elements is \( 2^n \).
- Here, \( n = 2 \).
- Therefore, the number of subsets of \( A \) is:
\[ 2^2 = 4 \]

3. **Determine the power set of set \( A \)**:
- The power set of a set is the set of all its subsets.
- Since \( A \) has 2 elements, the power set will have \( 2^n \) subsets, where \( n \) is the number of subsets of \( A \).
- The number of subsets of \( A \) is 4 (as calculated in step 2).
- Therefore, the number of subsets of the power set of \( A \) is:
\[ 2^4 = 16 \]

4. **Calculate the difference between the number of subsets of the power set and the number of subsets of set \( A \)**:
- Now, we need to find the difference:
\[ \text{Difference} = \text{Number of subsets of power set} - \text{Number of subsets of } A \]
- Substituting the values we found:
\[ \text{Difference} = 16 - 4 = 12 \]

5. **Conclusion**:
- The difference between the number of subsets of the power set and the number of subsets of set \( A \) is 12.

### Final Answer:
The difference is **12**.