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The problem asks to shade the region corresponding to \((A' \cup B) \cap C'\) on the Venn diagram. Here's how to interpret and approach it:

1. **\(A'\)** represents everything outside set \(A\).
2. **\(B\)** represents everything inside set \(B\).
3. **\(A' \cup B\)** means everything outside \(A\) or everything inside \(B\). This includes all regions in \(B\) and the areas outside \(A\).
4. **\(C'\)** represents everything outside set \(C\).
5. **\((A' \cup B) \cap C'\)** means the region that is both in \((A' \cup B)\) and outside of \(C\). So, you need to find the overlap between the two conditions.

### Steps to Shade the Diagram:
- First, identify the region for \(A' \cup B\), which includes all of \(B\) and areas outside \(A\).
- Next, identify the region for \(C'\), which is outside of \(C\).
- The final shading should cover the parts of \(A' \cup B\) that are also in \(C'\), i.e., the parts of \(B\) and outside \(A\) that are not within \(C\).

You can now shade the region where these two sets overlap on the Venn diagram.

Do you want a more detailed explanation or further help with shading?

Here are 5 related questions to explore:
1. How do we interpret the complement of a set in Venn diagrams?
2. What does the union of two sets represent in set theory?
3. How do intersection and union operations differ visually on a Venn diagram?
4. Can the same process apply to more than three sets in a Venn diagram?
5. How would the result change if the intersection were between \(A \cup B\) and \(C\), instead of using complements?

**Tip:** When working with Venn diagrams, always break down the logical operations step-by-step to ensure accuracy in shading the required regions.

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

This problem involves shading the region representing (A' ∪ B) ∩ C' on a Venn diagram. It covers key set theory concepts, including set complements, unions, and intersections. Suitable for high school students in Grades 9-12.

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