2.	Let 𝑈, 𝐴, and 𝐵 be nonempty sets such that 𝐴 ∩ 𝐵 is not empty.  Draw a Venn diagram shading the region corresponding to (𝑨 ∩ 𝑩̅) 	 
 


To represent the set \( A \cap \overline{B} \) using a Venn diagram, we need to follow these steps:

### Understanding the Expression:
- \( A \) is a subset of the universal set \( U \).
- \( B \) is another subset of \( U \), which overlaps with \( A \) because \( A \cap B \neq \emptyset \).
- \( \overline{B} \) is the complement of \( B \), meaning all elements in the universal set \( U \) that are **not** in \( B \).
- The intersection \( A \cap \overline{B} \) represents the elements that are in \( A \) but **not** in \( B \).

### Venn Diagram Description:
- Draw two overlapping circles within a rectangle representing the universal set \( U \).
- Label one circle as \( A \) and the other as \( B \).
- \( A \cap \overline{B} \) corresponds to the part of circle \( A \) that does not overlap with circle \( B \). This means you need to shade the region of \( A \) that lies **outside** \( B \).

Would you like me to generate a visual representation of this Venn diagram? 

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Here are 5 related questions for further exploration:
1. What does the region \( A \cap B \) represent on a Venn diagram?
2. How would you represent \( A \cup B \) on the Venn diagram?
3. What is the difference between \( A \cap B \) and \( A \cap \overline{B} \)?
4. What happens if \( A \) and \( B \) are disjoint? How would \( A \cap \overline{B} \) look then?
5. How do you represent \( \overline{A \cup B} \) on the diagram?

**Tip:** The complement of a set \( B \) (denoted \( \overline{B} \)) includes all elements that are outside of \( B \) in the universal set.

Let U, A, and B be nonempty sets such that A ∩ B is not empty. Draw a Venn diagram shading the region corresponding to (A ∩ B̅).

Learn how to shade the region corresponding to A ∩ B̅ in a Venn diagram. This problem involves understanding set theory concepts like intersection and complement. Suitable for students in Grades 9-12.

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