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The problem asks to select the regions corresponding to the set \( (A \cap B) \cup C \), referring to the Venn diagram provided.

Let's break this down:

1. **\( A \cap B \)**: This represents the intersection of sets \( A \) and \( B \), which means elements that are in both \( A \) and \( B \). In the Venn diagram, this corresponds to region **V** (the overlapping area of \( A \) and \( B \)).

2. **\( C \)**: This represents all elements in set \( C \). In the diagram, this includes regions **IV, V, VI, and VII** (the entire area within circle \( C \)).

3. **\( (A \cap B) \cup C \)**: This represents the union of the two sets \( A \cap B \) and \( C \). In terms of regions, it includes all the regions that are either in \( A \cap B \) or in \( C \).

So, the regions corresponding to \( (A \cap B) \cup C \) are:

- Region IV
- Region V
- Region VI
- Region VII

Would you like any further explanation or clarification?

Here are some related questions to explore:
1. What would be the regions corresponding to \( A \cup B \)?
2. What regions represent \( A \cap C \)?
3. How would you represent \( B \cap C \)?
4. What regions would represent \( (A \cup B) \cap C \)?
5. How would the regions change if you were asked for \( (A \cup C) \cap B \)?

**Tip**: When solving Venn diagram problems, always work through the intersections and unions step by step to ensure accuracy.

Select the regions that correspond to the set (A ∩ B) ∪ C based on the given Venn diagram.

Learn how to solve the set operation (A ∩ B) ∪ C using a Venn diagram. This solution includes detailed steps and visual breakdowns. Suitable for students in Grades 8-10, this problem covers key concepts in set theory.

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