If the number of items of a set A be n(A) = 40, n (B) = 26 and `n(A nn B) =16`, Then `n(AuuB)` is equal to

Options

A. 30
B. 40
C. 50
D. 60

Answer

To solve the problem, we need to find the number of elements in the union of two sets A and B, denoted as \( n(A \cup B) \). We can use the formula for the union of two sets:

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

Where:
- \( n(A) \) is the number of elements in set A,
- \( n(B) \) is the number of elements in set B,
- \( n(A \cap B) \) is the number of elements in the intersection of sets A and B.

### Step-by-step Solution:

1. **Identify the values given in the problem:**
- \( n(A) = 40 \)
- \( n(B) = 26 \)
- \( n(A \cap B) = 16 \)

2. **Substitute the values into the union formula:**
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
\[ n(A \cup B) = 40 + 26 - 16 \]

3. **Calculate the sum of \( n(A) \) and \( n(B) \):**
\[ 40 + 26 = 66 \]

4. **Subtract the intersection from the sum:**
\[ 66 - 16 = 50 \]

5. **Conclusion:**
\[ n(A \cup B) = 50 \]

Thus, the number of elements in the union of sets A and B is \( \boxed{50} \).