Question 5: The following Venn-Diagram shows 3 overlapping sets. Write an equation that will represent the union of the 3 sets (Make sure you use the intersection operation to remove the redundant elements from the union): B A
Question 5: The following Venn-Diagram shows 3 overlapping sets. Write an equation that will represent the union of the 3 sets (Make sure you use the intersection operation to remove the redundant elements from the union): B A
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Question 5:** The following Venn-Diagram shows 3 overlapping sets. Write an equation that will represent the union of the 3 sets (Make sure you use the intersection operation to remove the redundant elements from the union):
The diagram contains three overlapping circles labeled as \( A \), \( B \), and \( C \). These circles are drawn within a rectangle labeled \( S \), representing the universal set. Circle \( A \) overlaps with circles \( B \) and \( C \), and circles \( B \) and \( C \) also overlap with each other.
To write an equation for the union of sets \( A \), \( B \), and \( C \) while accounting for intersections, we use the formula:
\[
A \cup B \cup C = (A \cap B^c \cap C^c) \cup (A^c \cap B \cap C^c) \cup (A^c \cap B^c \cap C) \cup (A \cap B \cap C^c) \cup (A \cap B^c \cap C) \cup (A^c \cap B \cap C) \cup (A \cap B \cap C)
\]
This formula ensures each region within the Venn diagram is included in the union without redundancy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5362cbea-9427-4b2b-99cb-57a208edd853%2F37bc5bab-099e-48e5-99b0-924655bf6710%2Fnrbchtk_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 5:** The following Venn-Diagram shows 3 overlapping sets. Write an equation that will represent the union of the 3 sets (Make sure you use the intersection operation to remove the redundant elements from the union):
The diagram contains three overlapping circles labeled as \( A \), \( B \), and \( C \). These circles are drawn within a rectangle labeled \( S \), representing the universal set. Circle \( A \) overlaps with circles \( B \) and \( C \), and circles \( B \) and \( C \) also overlap with each other.
To write an equation for the union of sets \( A \), \( B \), and \( C \) while accounting for intersections, we use the formula:
\[
A \cup B \cup C = (A \cap B^c \cap C^c) \cup (A^c \cap B \cap C^c) \cup (A^c \cap B^c \cap C) \cup (A \cap B \cap C^c) \cup (A \cap B^c \cap C) \cup (A^c \cap B \cap C) \cup (A \cap B \cap C)
\]
This formula ensures each region within the Venn diagram is included in the union without redundancy.
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