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We are tasked with finding the set expression \( (C' \cup A) \cap B \), where:

- \( C' \) is the complement of set \( C \) within the universal set \( U \).
- \( \cup \) denotes union, and \( \cap \) denotes intersection.
- The sets are represented in the Venn diagram, with elements numbered.

### Step-by-Step Solution:

#### 1. **Find \( C' \):**
   - Set \( C \) contains the elements: \( \{2, 3, 4, 5\} \).
   - \( C' \) (the complement of \( C \)) includes all elements in \( U \) that are not in \( C \).
   - From the Venn diagram, \( C' = \{1, 6, 7, 8, 9\} \).

#### 2. **Find \( C' \cup A \):**
   - Set \( A \) contains the elements: \( \{1, 3, 4, 5, 6\} \).
   - The union of \( C' \) and \( A \) includes all elements from both sets:
     \[
     C' \cup A = \{1, 3, 4, 5, 6, 7, 8, 9\}
     \]

#### 3. **Find \( (C' \cup A) \cap B \):**
   - Set \( B \) contains the elements: \( \{5, 6, 8, 9\} \).
   - The intersection includes elements that are both in \( C' \cup A \) and \( B \):
     \[
     (C' \cup A) \cap B = \{5, 6, 8, 9\}
     \]

### Final Answer:
\[
(C' \cup A) \cap B = \{5, 6, 8, 9\}
\]

Would you like more details or have any questions?

Here are 5 related questions you could explore:
1. What is the union of \( A \) and \( B \)?
2. How would the solution change if we were asked to find \( (C \cap A') \cup B \)?
3. What are the elements of \( A' \cap B \)?
4. Can you list the elements of \( A \cup B \cup C \)?
5. What is the complement of \( B \)?

**Tip:** When working with Venn diagrams, focus on one operation at a time (union, intersection, complement) to avoid confusion!

This page provides a step-by-step solution to the set theory problem (C' ∪ A) ∩ B, using a Venn diagram to illustrate the process. Suitable for students in Grades 8-10, the solution involves applying basic set theory rules like union, intersection, and complement.

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