The expression \((A \cup B)' \cap C\) represents a set-theoretic operation involving the union, complement, and intersection of sets. Here's a breakdown of how to evaluate this:

1. **\( A \cup B \)**: This is the union of sets \(A\) and \(B\), which includes all elements that are in either \(A\), \(B\), or both.

2. **\( (A \cup B)' \)**: This represents the complement of \( A \cup B \), which includes all elements **not** in the union of \(A\) and \(B\). In other words, it contains elements that are outside both \(A\) and \(B\).

3. **\( (A \cup B)' \cap C \)**: Now, this is the intersection of \( (A \cup B)' \) with \(C\). This means we're looking for all elements that are in \(C\), but also **not** in \(A \cup B\).

### Interpretation:
- You're finding elements that belong to set \(C\) but do not belong to either set \(A\) or set \(B\).
  
If you have specific sets for \(A\), \(B\), and \(C\), you can directly compute the resulting set.

Would you like a detailed example with specific sets or further clarification?

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**Relative Questions:**

1. How is the union of sets \(A\) and \(B\) different from their intersection?
2. What is the difference between a complement and an intersection in set theory?
3. Can you give an example where \(A \cup B = A \cap B\)?
4. What are De Morgan's laws in set theory, and how do they apply here?
5. How would the operation change if we used \(A \cap B\) instead of \(A \cup B\)?

**Tip**: Always use Venn diagrams when working with set operations to visually interpret the relationships!

Explore the set-theoretic operation (A ∪ B)' ∩ C with a detailed explanation. This problem involves understanding the union, complement, and intersection of sets, as well as applying De Morgan's Laws. Suitable for high school students in Grades 9-12.

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