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### Given:
- **Universal Set \( U \)**: \(\{1, 2, 3, \dots, 18, 19, 20\}\)
- **Set \( A \)**: \(\{2, 3, 4, 5, 7, 12, 13, 14, 18, 20\}\)
- **Set \( B \)**: \(\{1, 5, 11, 13, 15, 19, 20\}\)
- **Set \( C \)**: \(\{1, 3, 5, 6, 10, 15, 19, 20\}\)

We are required to determine the following:

1. \( n(A) \) - the number of elements in Set \( A \).
2. \( n(B) \) - the number of elements in Set \( B \).
3. \( n(A \cap B) \) - the number of elements in the intersection of Sets \( A \) and \( B \).
4. \( n(B \cap C) \) - the number of elements in the intersection of Sets \( B \) and \( C \).
5. \( n(A \cup C) \) - the number of elements in the union of Sets \( A \) and \( C \).

### Solution:

1. **\( n(A) \)**: Count the elements in Set \( A \).
   - \( A = \{2, 3, 4, 5, 7, 12, 13, 14, 18, 20\} \)
   - Number of elements = **10**

2. **\( n(B) \)**: Count the elements in Set \( B \).
   - \( B = \{1, 5, 11, 13, 15, 19, 20\} \)
   - Number of elements = **7**

3. **\( n(A \cap B) \)**: Find the intersection of Sets \( A \) and \( B \), then count the elements.
   - \( A \cap B = \{5, 13, 20\} \)
   - Number of elements = **3**

4. **\( n(B \cap C) \)**: Find the intersection of Sets \( B \) and \( C \), then count the elements.
   - \( B \cap C = \{1, 5, 15, 19, 20\} \)
   - Number of elements = **5**

5. **\( n(A \cup C) \)**: Find the union of Sets \( A \) and \( C \), then count the elements.
   - \( A \cup C = \{1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 18, 19, 20\} \)
   - Number of elements = **15**

### Final Answers:

1. \( n(A) = 10 \)
2. \( n(B) = 7 \)
3. \( n(A \cap B) = 3 \)
4. \( n(B \cap C) = 5 \)
5. \( n(A \cup C) = 15 \)

Would you like any further details or explanations on these calculations?

### Related Questions:

1. What is the complement of set \( A \) in the universal set \( U \)?
2. How would you find the intersection of sets \( A \), \( B \), and \( C \)?
3. What is the union of sets \( B \) and \( C \)?
4. How many elements are in the set \( A \cap C \)?
5. What is the symmetric difference between sets \( A \) and \( C \)?

### Tip:
When dealing with multiple sets, Venn diagrams can be particularly helpful to visualize intersections and unions effectively.

Let U = {1, 2, 3, ..., 20} be the universal set. Let sets A, B, and C be subsets of U, where A = {2, 3, 4, 5, 7, 12, 13, 14, 18, 20}, B = {1, 5, 11, 13, 15, 19, 20}, and C = {1, 3, 5, 6, 10, 15, 19, 20}. Determine the following: n(A), n(B), n(A ∩ B), n(B ∩ C), n(A ∪ C).

Learn how to solve a problem involving sets, subsets, intersections, unions, and cardinality. This problem explores set operations using basic set theory and is suitable for high school students. The universal set includes numbers 1 through 20, and three subsets are analyzed to find cardinalities of unions and intersections.

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