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To define set \( A \) in terms of \( B \) and \( B' \) (the complement of \( B \)), we observe the following from the Venn diagram:

- Set \( A \) is the circle on the left.
- Part of \( A \) overlaps with \( B \), and part of \( A \) is outside of \( B \), but still within the universal set \( U \).
  
Therefore, the set \( A \) can be expressed as:
\[ A = (A \cap B') \cup (A \cap B) \]

This states that set \( A \) includes both the parts of \( A \) that do not intersect with \( B \) (i.e., \( A \cap B' \)) and the parts that do intersect with \( B \) (i.e., \( A \cap B \)).

Let me know if you'd like more details or have any questions.

Here are five related questions to explore further:
1. How would you define set \( B \) in terms of \( A \) and \( A' \)?
2. What is the complement of set \( A \) in terms of \( B \) and \( B' \)?
3. How can the universal set \( U \) be expressed using sets \( A \), \( B \), and their complements?
4. How can the intersection \( A \cap B \) be expressed using set operations?
5. What is the relationship between \( A \cup B \) and the universal set \( U \)?

**Tip:** In Venn diagrams, intersections and unions help visually represent how different sets overlap and relate to each other within a universal set.

Write an expression that defines set A in terms of B and B'.

Discover how to define set A in terms of sets B and B' using Venn diagrams. This problem focuses on key set theory concepts, including unions and intersections, and is perfect for students in Grades 9-12.

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