Explanation Given: The given statement is: n ( A ) = 54 , n ( A ∩ B ) = 22 , n ( A ∪ B ) = 85 , n ( A ∩ B ∩ C ) = 4 , n ( A ∩ C ) = 15 , n ( B ∩ C ) = 16 , n ( C ) = 44 , n ( B ′ ) = 63 Consider the statement is: n ( A ) = 54 , n ( A ∩ B ) = 22 , n ( A ∪ B ) = 85 , n ( A ∩ B ∩ C ) = 4 , n ( A ∩ C ) = 15 , n ( B ∩ C ) = 16 , n ( C ) = 44 , n ( B ′ ) = 63 We start with n ( A ∩ B ∩ C ) = 4 , If n ( A ∩ B ) = 15 , an additional 4 are in A ∩ B ∩ C so n ( A ∩ B ′ ∩ C ) = 11 . Similarly, n ( B ∩ C ) = 16 , an additional 4 are in A ∩ B ∩ C so n ( B ∩ C ∩ A ′ ) = 12 , n ( C ) = 44

2nd Edition

ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

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Chapter 12.1, Problem 66E

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The Venn diagram and fill in the number of element for each region for n(A)=54,n(A∩B)=22,n(A∪B)=85,n(A∩B∩C)=4,n(A∩C)=15,n(B∩C)=16,n(C)=44,n(B′)=63

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Chapter 12.1, Problem 65E

Chapter 12.1, Problem 67E

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To draw: The Venn diagram and fill in the number of element for each region for n ( A ) = 54 , n ( A ∩ B ) = 22 , n ( A ∪ B ) = 85 , n ( A ∩ B ∩ C ) = 4 , n ( A ∩ C ) = 15 , n ( B ∩ C ) = 16 , n ( C ) = 44 , n ( B ′ ) = 63

Solution Summary: The author illustrates the Venn diagram and fill in the number of element for each region for the given conditions.

Concept explainers

To draw:

The Venn diagram and fill in the number of element for each region for n(A)=54,n(A∩B)=22,n(A∪B)=85,n(A∩B∩C)=4,n(A∩C)=15,n(B∩C)=16,n(C)=44,n(B′)=63

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Chapter 12 Solutions

To draw: The Venn diagram and fill in the number of element for each region for n ( A ) = 54 , n ( A ∩ B ) = 22 , n ( A ∪ B ) = 85 , n ( A ∩ B ∩ C ) = 4 , n ( A ∩ C ) = 15 , n ( B ∩ C ) = 16 , n ( C ) = 44 , n ( B ′ ) = 63

Solution Summary: The author illustrates the Venn diagram and fill in the number of element for each region for the given conditions.

Concept explainers

To draw: The Venn diagram and fill in the number of element for each region for n(A)=54,n(A∩B)=22,n(A∪B)=85,n(A∩B∩C)=4,n(A∩C)=15,n(B∩C)=16,n(C)=44,n(B′)=63

Want to see the full answer?

Chapter 12 Solutions

To draw:

The Venn diagram and fill in the number of element for each region for n(A)=54,n(A∩B)=22,n(A∪B)=85,n(A∩B∩C)=4,n(A∩C)=15,n(B∩C)=16,n(C)=44,n(B′)=63