Which regions represent set ANC?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Using Venn Diagrams to Illustrate Set Intersections**
To understand how sets intersect with each other, we can use Venn diagrams. Below is a Venn diagram that includes three sets, \( A \), \( B \), and \( C \), along with their universal set \( U \).
![Venn Diagram]
In this diagram:
- Circle \( A \) is represented by the regions labeled I, II, IV, and V.
- Circle \( B \) contains the regions II, III, V, and VI.
- Circle \( C \) includes the regions IV, V, VI, and VII.
Each intersection of circles represents the common elements between the sets:
- **Region II**: The intersection of sets \( A \) and \( B \) only.
- **Region IV**: The intersection of sets \( A \) and \( C \) only.
- **Region VI**: The intersection of sets \( B \) and \( C \) only.
- **Region V**: The intersection of all three sets \( A \), \( B \), and \( C \).
To determine the intersection regions of sets \( A \) and \( C \) (denoted as \( A \cap C \)), we need to identify the regions that are part of both \( A \) and \( C \).
From the diagram:
- Region IV belongs to both \( A \) and \( C \).
- Region V belongs to all three sets including both \( A \) and \( C \).
Therefore, **the regions representing the set \( A \cap C \) are IV and V.**
By visually inspecting the Venn diagram, we can easily find the common areas (intersections) between different sets, which helps in understanding their relationships effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F432470f7-8687-4754-a4cb-bb73439b103d%2Fdc3819fc-a07a-45fb-9fbd-d0d582cbe052%2F0ovpcno_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Venn Diagrams to Illustrate Set Intersections**
To understand how sets intersect with each other, we can use Venn diagrams. Below is a Venn diagram that includes three sets, \( A \), \( B \), and \( C \), along with their universal set \( U \).
![Venn Diagram]
In this diagram:
- Circle \( A \) is represented by the regions labeled I, II, IV, and V.
- Circle \( B \) contains the regions II, III, V, and VI.
- Circle \( C \) includes the regions IV, V, VI, and VII.
Each intersection of circles represents the common elements between the sets:
- **Region II**: The intersection of sets \( A \) and \( B \) only.
- **Region IV**: The intersection of sets \( A \) and \( C \) only.
- **Region VI**: The intersection of sets \( B \) and \( C \) only.
- **Region V**: The intersection of all three sets \( A \), \( B \), and \( C \).
To determine the intersection regions of sets \( A \) and \( C \) (denoted as \( A \cap C \)), we need to identify the regions that are part of both \( A \) and \( C \).
From the diagram:
- Region IV belongs to both \( A \) and \( C \).
- Region V belongs to all three sets including both \( A \) and \( C \).
Therefore, **the regions representing the set \( A \cap C \) are IV and V.**
By visually inspecting the Venn diagram, we can easily find the common areas (intersections) between different sets, which helps in understanding their relationships effectively.
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