https://file.aiquickdraw.com/mathbot/file/17273871004517b63ucpi.jpg

The Venn diagram depicts two sets, \( A \) and \( B \), within a universal set \( U \). In this diagram, the unshaded region is inside set \( A \) but outside set \( B \), which corresponds to \( A - B \) (or \( A \setminus B \)).

Let's analyze the options:

1. **\( A \cap B \)**: This represents the intersection of \( A \) and \( B \), the area where the two sets overlap. However, this region is not shaded in the diagram.

2. **\( A - B \)**: This is the difference between sets \( A \) and \( B \), meaning the part of \( A \) that is not in \( B \). This region is shaded in the diagram.

3. **\( (A \cup B)' \)**: This represents the complement of the union of \( A \) and \( B \), which would include everything outside both \( A \) and \( B \). This does not match the shaded region.

4. **\( A' \cup B \)**: This is the union of the complement of \( A \) and \( B \), which would shade everything outside \( A \) plus all of \( B \). This does not match the shaded area either.

Given the diagram, the correct set-theoretic expression is:

**\( A - B \)**.

Let me know if you'd like further details, and here are some related questions to think about:

1. What does \( A \cup B \) represent in a Venn diagram?
2. How would the Venn diagram look if it depicted \( B - A \)?
3. What would the shading be for \( A' \cap B \)?
4. How can we represent the universal set \( U \) in a Venn diagram?
5. Can the complement of a set be visualized using just two sets?

**Tip**: Set difference \( A - B \) can also be written as \( A \cap B' \), highlighting the part of \( A \) that doesn't intersect with \( B \).

Which of the set theoretic expressions below has the following Venn diagram?

Learn how to solve a set theory problem using Venn diagrams, specifically illustrating the set difference A - B. Explore core concepts such as intersections, complements, and set operations. Suitable for high school students in Grades 9-12.

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