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The image shows a question related to set operations and Venn diagrams, asking to choose the correct set notation to describe the shaded region in the Venn diagram. The symbols \(A\), \(B\), \(C\), \(\cup\) (union), and \(\cap\) (intersection) are used in the choices. There is a Venn diagram with three intersecting circles labeled \(A\), \(B\), and \(C\), and a portion is shaded.

To help you identify the correct answer, let me analyze the Venn diagram:
1. \(A\), \(B\), and \(C\) are sets.
2. The shaded area corresponds to the parts of the sets involved in the union and intersection operations.

Let me break down each option:

- \(A \cap (B \cup C)\): This represents the intersection of set \(A\) with the union of sets \(B\) and \(C\).
- \(A \cup (B \cap C)\): This represents the union of set \(A\) with the intersection of sets \(B\) and \(C\).
- \((A \cup B) \cap C\): This represents the intersection of set \(C\) with the union of sets \(A\) and \(B\).
- \((A \cap B) \cup C\): This represents the union of set \(C\) with the intersection of sets \(A\) and \(B\).
- \(B \cap (C \cup A)\): This represents the intersection of set \(B\) with the union of sets \(C\) and \(A\).

To provide a more specific solution, I need to closely examine which regions of the Venn diagram are shaded. Based on the provided diagram and answer choices, you can match the shading with the appropriate set operation.

Would you like a more detailed breakdown of each option, or is there anything specific you'd like to clarify further? Here are 5 related questions for exploration:

1. How do union and intersection operations differ in set theory?
2. How can a Venn diagram visually represent set operations?
3. What does the complement of a set represent in a Venn diagram?
4. Can a set be a subset of itself, and how is that represented?
5. How are multiple set operations evaluated when parentheses are involved?

**Tip**: Always start by simplifying expressions within parentheses in set operations, as they act similarly to arithmetic operations.

Choose the correct set operation for the shaded region in the Venn diagram using the symbols A, B, C, ∪ (union), ∩ (intersection).

Explore set operations using Venn diagrams. This problem asks you to determine the correct set notation for the shaded region, using concepts of union and intersection. Suitable for students in Grades 9-12, it covers essential set theory operations.

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