Let A and B be two sets such that `n (A) = 52, n (B) = 60 and n(A nn B) = 16. ` Draw a Venn diagram and find
`n(A uuB ) `

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 are given the following information:

- \( n(A) = 52 \)
- \( n(B) = 60 \)
- \( n(A \cap B) = 16 \)

### Step 1: Use the formula for the union of two sets
The formula for the number of elements in the union of two sets is given by:

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

### Step 2: Substitute the given values into the formula
Now, we substitute the values we have into the formula:

\[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \]
\[ n(A \cup B) = 52 + 60 - 16 \]

### Step 3: Perform the arithmetic
Now we perform the addition and subtraction:

\[ n(A \cup B) = 112 - 16 \]
\[ n(A \cup B) = 96 \]

### Conclusion
Thus, the number of elements in the union of sets A and B is:

\[ n(A \cup B) = 96 \]

### Venn Diagram
To draw the Venn diagram:
1. Draw a rectangle to represent the universal set \( U \).
2. Draw two overlapping circles inside the rectangle. Label one circle as set \( A \) and the other as set \( B \).
3. In the overlapping area (the intersection), write the number of elements in \( A \cap B \), which is 16.
4. In the part of circle \( A \) that does not overlap with circle \( B \), write \( n(A) - n(A \cap B) = 52 - 16 = 36 \).
5. In the part of circle \( B \) that does not overlap with circle \( A \), write \( n(B) - n(A \cap B) = 60 - 16 = 44 \).