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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)

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
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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**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.
Transcribed Image Text:**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. \( (A \cup B^c) \cup (A^c \cup B) \)
Transcribed Image Text:**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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