To find the number of elements in the union of sets \( A \) and \( B \), denoted as \( n(A \cup B) \), we count all the unique elements within both sets \( A \) and \( B \) without double-counting those that appear in the intersection.

### Elements in \( A \) (from the diagram):
- 9, 15, \( d \), \( b \), 5, \( c \)

### Elements in \( B \) (from the diagram):
- \( x \), 31, 12, \( f \), 5, \( c \)

### Union of \( A \) and \( B \) (combine all unique elements):
- \( A \cup B = \{9, 15, d, b, 5, c, x, 31, 12, f\} \)

Now, let's count these unique elements:

- \( 9, 15, d, b, 5, c, x, 31, 12, f \) 

This gives us a total of **10 elements**.

Thus, \( n(A \cup B) = 10 \).

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### Further Questions:
1. What is \( n(A \cap B) \), the number of elements in the intersection of \( A \) and \( B \)?
2. How would you calculate \( n(A) \) and \( n(B) \) individually?
3. What is the number of elements in the set difference \( A - B \)?
4. What are the elements in the symmetric difference \( A \triangle B \)?
5. How many elements are there in the universal set \( U \)? 

**Tip:** When working with unions and intersections, always pay attention to overlapping elements to avoid double-counting.

Learn how to calculate the number of elements in the union of sets A and B, denoted as n(A ∪ B). This problem covers key concepts in set theory, including union, intersection, set difference, and symmetric difference. Suitable for students in Grades 9-12.

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