If `n(A)= 15, n(B)= 20, n(A nn B)=10`, then `n(A uu B)` is equal to

Options

A. 55
B. 30
C. 5
D. None of these

Answer

To solve the problem, we need to find the value of \( n(A \cup B) \) using the given values of \( n(A) \), \( n(B) \), and \( n(A \cap B) \).

### Step-by-Step Solution:

1. **Identify the given values:**
- \( n(A) = 15 \)
- \( n(B) = 20 \)
- \( n(A \cap B) = 10 \)

2. **Write down the formula for the union of two sets:**
- The formula for the number of elements in the union of two sets is:
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]

3. **Substitute the values into the formula:**
- Now, we substitute the known values into the formula:
\[ n(A \cup B) = 15 + 20 - 10 \]

4. **Perform the calculations:**
- First, add \( n(A) \) and \( n(B) \):
\[ 15 + 20 = 35 \]
- Then, subtract \( n(A \cap B) \):
\[ 35 - 10 = 25 \]

5. **Conclusion:**
- Therefore, the value of \( n(A \cup B) \) is:
\[ n(A \cup B) = 25 \]

### Final Answer:
\( n(A \cup B) = 25 \)