https://r2.erweima.ai/mathbot/image/1726613374947urs2tw5p.jpg

Let's analyze the image and solve the questions based on the Venn diagram involving three sets \( A \), \( B \), and \( C \).

### Venn Diagram Analysis:
- The diagram has numbers distributed across different intersections of the three sets \( A \), \( B \), and \( C \).
- The regions of the sets are as follows:
  - Set \( A \) contains the numbers: \( 0, 3, 4, 1, 2, 5 \).
  - Set \( B \) contains the numbers: \( 7, 6, 2, 5 \).
  - Set \( C \) contains the numbers: \( 4, 8, 5, 2 \).

### Now, let's answer the questions:

#### (a) Elements of \( A \)
- \( A = \{ 0, 1, 2, 3, 4, 5 \} \)

#### (b) Elements of \( B \)
- \( B = \{ 2, 5, 6, 7 \} \)

#### (c) Elements of \( C \)
- \( C = \{ 2, 4, 5, 8 \} \)

#### (d) Elements of \( (A \cap B) \cup (B \cap C) \)
- \( A \cap B \) means elements common to both \( A \) and \( B \): \( A \cap B = \{ 2, 5 \} \).
- \( B \cap C \) means elements common to both \( B \) and \( C \): \( B \cap C = \{ 2, 5 \} \).
- Now, the union \( (A \cap B) \cup (B \cap C) = \{ 2, 5 \} \).

#### (e) Elements of \( (A \cap C) \cup B \)
- \( A \cap C \) means elements common to both \( A \) and \( C \): \( A \cap C = \{ 2, 4, 5 \} \).
- Now, \( (A \cap C) \cup B = \{ 2, 4, 5 \} \cup \{ 2, 5, 6, 7 \} = \{ 2, 4, 5, 6, 7 \} \).

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If you have any questions or want further explanations, feel free to ask!

### 5 Related Questions:
1. What are the elements of \( A \cap B \cap C \)?
2. How do you compute the complement of \( A \), \( B \), or \( C \) in this Venn diagram?
3. What is the result of \( A \cup B \cup C \)?
4. How do you find \( (A \cup B) \cap C \)?
5. Can you explain how the distributive law works in set theory?

### Tip:
Always remember to calculate intersections before unions when dealing with complex set expressions.

Observe the diagram and answer the following questions regarding sets A, B, and C.

Learn how to analyze and solve questions based on a Venn diagram involving three sets A, B, and C. Understand set operations such as intersection and union. Suitable for students in Grades 8-10.

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