The expression \((A \setminus B) \cup C\) represents a set operation involving the sets \(A\), \(B\), and \(C\). Here's a breakdown of the operation:

1. **\(A \setminus B\) (A minus B)**: This is the set of elements that are in \(A\) but not in \(B\).
   \[
   A \setminus B = \{x \in A \mid x \notin B\}
   \]
2. **\(\cup C\) (Union with C)**: After finding \(A \setminus B\), the result is then unioned with \(C\). The union operation combines all elements from both sets without duplication.

Thus, the result is:
\[
(A \setminus B) \cup C = \{x \in A \mid x \notin B\} \cup C
\]

### Simplified Interpretation:
- Take all the elements that are in \(A\) but not in \(B\).
- Combine those elements with all the elements in \(C\), ensuring no element is duplicated.

Would you like to see an example with specific sets? Or perhaps more detailed steps?

### Related Questions:
1. What is the difference between \(A \setminus B\) and \(B \setminus A\)?
2. How does intersection \(\cap\) differ from union \(\cup\)?
3. What happens if \(A = B\) in \(A \setminus B\)?
4. Can \(\setminus\) be distributed over union or intersection?
5. How do we interpret the union of three or more sets?

### Tip:
Remember that set operations like union \(\cup\) and difference \(\setminus\) are fundamental tools in set theory and can be visualized using Venn diagrams to aid understanding.

Explore the set theory operation (A ∖ B) ∪ C, breaking down how to compute the set difference and union of sets A, B, and C. Learn about key concepts in set theory, such as set difference and union, with clear explanations and formulas. Suitable for high school students in Grades 9-12.

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