If `n ( A ) = 20, n ( B ) = 10 , n ( A cap B ) = 25`, then `n ( A cup 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 number of elements in the union of sets A and B, denoted as \( n(A \cup B) \). We will use the formula for the union of two sets:

\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]

### Step-by-step Solution:

1. **Identify the values given in the problem:**
- \( n(A) = 20 \)
- \( n(B) = 10 \)
- \( n(A \cap B) = 25 \)

2. **Substitute the values into the formula:**
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
\[ n(A \cup B) = 20 + 10 - 25 \]

3. **Perform the addition and subtraction:**
\[ n(A \cup B) = 30 - 25 \]
\[ n(A \cup B) = 5 \]

4. **Conclusion:**
The number of elements in the union of sets A and B is \( n(A \cup B) = 5 \).

### Final Answer:
\[ n(A \cup B) = 5 \]