**Title: Understanding Venn Diagrams and Set Notations**---### Problem Statement:Write an expression describing the shaded portion(s) of the Venn diagram.### Explanation of the Venn Diagram:The diagram consists of two overlapping circles within a rectangle labeled $ U $, which represents the universal set. The left circle is labeled $ A $ and the right circle is labeled $ B $. The overlapping region of circles $ A $ and $ B $ is shaded, indicating the intersection of sets $ A $ and $ B $.### Multiple Choice Options:- $ A^c \cap B^c $- $(A \cap B)^c$ (correct answer, as indicated by the filled circle)- $ (A \cap B^c) \cup (A^c \cap B) $- $ (A \cap B^c) \cap (A^c \cap B) $- $ (A \cup B^c) \cup (A^c \cup B) $### Explanation of Correct Answer:The correct expression for the shaded region, which is the intersection of sets $ A $ and $ B $, is $(A \cap B)$. This indicates the common elements shared by both sets $ A $ and $ B $.---Using Venn diagrams helps to visualize the relationships between different sets and understand how they interact through operations like union, intersection, and complement. **Diagram Explanation:**The image shows a Venn diagram within a rectangular box labeled $ U $, representing the universal set. Inside the box, there are two overlapping circles labeled $ A $ and $ B $. The overlap between sets $ A $ and $ B $ is the intersection area of the two circles.**Multiple Choice Options:**1. $ A^c \cap B^c $2. $ (A \cap B)^c $3. $ (A \cap B^c) \cup (A^c \cap B) $4. $ (A \cap B^c) \cap (A^c \cap B) $5. $ (A \cup B^c) \cup (A^c \cup B) $

a) From the venn diagram A∩Bc

Answered: Write an expression describing the…

Write an expression describing the shaded portion(s) of the Venn diagram. (a) U A B O A n BC (A n B)C O (A n Bº) U (A° n B) O (A n BC) n (A° n B) O (AU B) U (AC U B)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

**Title: Understanding Venn Diagrams and Set Notations**

---

### Problem Statement:
Write an expression describing the shaded portion(s) of the Venn diagram.

### Explanation of the Venn Diagram:

The diagram consists of two overlapping circles within a rectangle labeled $ U $, which represents the universal set. The left circle is labeled $ A $ and the right circle is labeled $ B $. The overlapping region of circles $ A $ and $ B $ is shaded, indicating the intersection of sets $ A $ and $ B $.

### Multiple Choice Options:

- $ A^c \cap B^c $
- $(A \cap B)^c$ (correct answer, as indicated by the filled circle)
- $ (A \cap B^c) \cup (A^c \cap B) $
- $ (A \cap B^c) \cap (A^c \cap B) $
- $ (A \cup B^c) \cup (A^c \cup B) $

### Explanation of Correct Answer:

The correct expression for the shaded region, which is the intersection of sets $ A $ and $ B $, is $(A \cap B)$. This indicates the common elements shared by both sets $ A $ and $ B $.

---

Using Venn diagrams helps to visualize the relationships between different sets and understand how they interact through operations like union, intersection, and complement.

**Diagram Explanation:**

The image shows a Venn diagram within a rectangular box labeled $ U $, representing the universal set. Inside the box, there are two overlapping circles labeled $ A $ and $ B $. The overlap between sets $ A $ and $ B $ is the intersection area of the two circles.

**Multiple Choice Options:**

1. $ A^c \cap B^c $
2. $ (A \cap B)^c $
3. $ (A \cap B^c) \cup (A^c \cap B) $
4. $ (A \cap B^c) \cap (A^c \cap B) $
5. $ (A \cup B^c) \cup (A^c \cup B) $

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