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The problem asks to shade \( B \cup (C \cap A')' \) on the Venn diagram. Let's break this expression down step by step:

1. **\( A' \)**: This represents the complement of set \( A \), meaning all the elements outside of set \( A \) (in the universal set \( U \)).

2. **\( C \cap A' \)**: This is the intersection of set \( C \) and \( A' \), which refers to the elements that are in set \( C \) but not in set \( A \).

3. **\( (C \cap A')' \)**: This is the complement of \( C \cap A' \), meaning it includes everything in the universal set \( U \) except the elements in \( C \cap A' \).

4. **\( B \cup (C \cap A')' \)**: Finally, this is the union of set \( B \) and the complement of \( C \cap A' \). So, you need to shade all the areas that belong to set \( B \) as well as the areas outside of \( C \cap A' \).

Now, referring to the Venn diagram:

- First, identify \( C \cap A' \), which is the part of set \( C \) that does not overlap with set \( A \).
- Then, take the complement of that region, which would be everything except that part of set \( C \) and outside of set \( A \).
- Finally, shade all of set \( B \) in the diagram and also include the regions that are part of the complement of \( C \cap A' \).

This approach will give you the correct shaded area for \( B \cup (C \cap A')' \).

Do you want more details or have any questions?

Here are 5 related questions:
1. What is the union of two sets in a Venn diagram?
2. How do you represent a complement of a set in Venn diagrams?
3. How does an intersection of two sets appear in a Venn diagram?
4. How do we shade multiple sets on a Venn diagram that include both union and intersection?
5. What happens when we take the complement of an intersection?

**Tip:** To master Venn diagrams, always break down complex expressions step by step to visualize each part clearly.

Shade B ∪ (C ∩ A')' on the Venn diagram.

Learn how to shade B ∪ (C ∩ A')' on a Venn diagram with a step-by-step explanation. This problem explores key concepts in set theory, including union, intersection, and complement of sets. Ideal for students in Grades 8-10.

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