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To solve this problem, we need to express each target set using the provided sets \( A \), \( B \), \( C \), and the universal set \( U \), with operations including union, intersection, absolute difference, and relative difference.

Given sets:
- \( A = \{1, 2, 4, 7, 8\} \)
- \( B = \{1, 4, 5, 7, 9\} \)
- \( C = \{3, 7, 8, 9\} \)
- \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)

We need to find expressions for the sets:
1. (a) \(\{2, 7, 9\}\)
2. (b) \(\{3, 5, 6, 7, 9, 10\}\)

### Solution

#### (a) Set \(\{2, 7, 9\}\)
1. **Identify common elements in sets**:
   - \(2\) is in \(A\).
   - \(7\) is in \(A\), \(B\), and \(C\).
   - \(9\) is in \(B\) and \(C\).
   
2. **Construct an expression**:
   - Since \(7\) is common to all three sets, we need to isolate \(2\) and \(9\) appropriately. We can start by considering intersections and relative differences.
   - A possible approach:
     \[
     (A \cup B) \cap C
     \]

This will yield the set \(\{2, 7, 9\}\).

#### (b) Set \(\{3, 5, 6, 7, 9, 10\}\)
1. **Identify common elements**:
   - \(3\) and \(9\) are in \(C\).
   - \(5\) and \(7\) are in \(B\).
   - \(6\) and \(10\) are only in the universal set \( U \) but not in \(A\), \(B\), or \(C\).
   
2. **Construct an expression**:
   - Start by considering the elements that are not in \(A\) but are in \(U\), which can be represented as \(U - A\).
   
   Thus, we can write the expression as:
   \[
   U - A = \{3, 5, 6, 7, 9, 10\}
   \]

### Final Answers
- **(a)** \(\{2, 7, 9\} = (A \cup B) \cap C\)
- **(b)** \(\{3, 5, 6, 7, 9, 10\} = U - A\)

Would you like further explanation on these operations or have additional questions?

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Here are five related questions to explore further:
1. How would you find the union of all three sets \(A\), \(B\), and \(C\)?
2. What is the intersection of sets \(A\) and \(B\)?
3. How would you represent \(A - B\) using set operations?
4. How could we determine the symmetric difference between sets \(B\) and \(C\)?
5. What is the complement of \(C\) with respect to the universal set \(U\)?

**Tip:** When working with multiple sets and set operations, it can be helpful to visualize them using Venn diagrams for a clearer understanding of relationships.

Let A = {1, 2, 4, 7, 8}, B = {1, 4, 5, 7, 9}, and C = {3, 7, 8, 9}. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Find set expressions using these sets and the operations of union, intersection, absolute difference, and relative difference to represent the sets: (a) {2, 7, 9} (b) {3, 5, 6, 7, 9, 10}.

Explore how to represent specific sets using given sets A, B, C, and the universal set U with operations like union, intersection, and differences. This detailed explanation is suitable for high school students and covers core set theory concepts.

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