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The problem is asking you to shade the region representing \( B' \cup C \) on the Venn diagram.

### Step-by-step solution:
1. **Set \( B' \)**: \( B' \) represents the complement of set \( B \), which means everything in the universal set \( U \) **except** for the area inside circle \( B \). So, you'll need to shade **all areas outside circle \( B \)**, including \( C \) and any part of the universal set outside both circles.

2. **Set \( C \)**: The set \( C \) includes everything inside circle \( C \).

3. **Union \( B' \cup C \)**: The union \( \cup \) means we combine all regions that are in either \( B' \) or \( C \). So, this means you will shade:
   - All of \( C \), including its overlap with \( B \).
   - All areas outside \( B \), but inside the universal set \( U \).

In summary, you will shade:
- The entire region of \( C \) (the right circle).
- The region outside of \( B \), including the area around both circles.

Would you like more details on any part of this solution? Here are some related questions for you:

1. How do we interpret \( B' \) in relation to the universal set \( U \)?
2. What is the difference between union \( \cup \) and intersection \( \cap \)?
3. How would you represent \( B' \cap C \) on a Venn diagram?
4. What if the diagram had three sets instead of two? How would the union change?
5. Can you explain the difference between a universal set and a subset?

**Tip:** When solving Venn diagram problems, it's helpful to first identify the regions that are being excluded by any complements (e.g., \( B' \)).

Learn how to shade the region representing B' ∪ C on a Venn diagram. This problem covers important concepts in set theory, including union and complement of sets. Suitable for high school students (Grades 9-12).

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