If `n(AnnB)=40,n(A)=50`, and `n(B)=60`, then find `n(A uu B)`.

Answer

To find the number of elements in the union of sets A and 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:
- \( n(A \cup B) \) is the number of elements in the union of sets A and B.
- \( n(A) \) 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 given values:**
- \( n(A) = 50 \)
- \( n(B) = 60 \)
- \( n(A \cap B) = 40 \)

2. **Substitute the values into the formula:**
\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
\[ n(A \cup B) = 50 + 60 - 40 \]

3. **Calculate the sum of \( n(A) \) and \( n(B) \):**
\[ 50 + 60 = 110 \]

4. **Subtract the intersection from the sum:**
\[ 110 - 40 = 70 \]

5. **Conclusion:**
\[ n(A \cup B) = 70 \]

### Final Answer:
The number of elements in the union of sets A and B is \( n(A \cup B) = 70 \).