Explanation Given Information: The table given below shows the results of a survey of authors conducted by a fictitious publishing company, New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100 The set C represents the set of successful authors, the set U represents the set of unsuccessful authors, the set N represents the new authors and the set E represents set of established authors. Formula used: For union of sets X , with number of elements n ( X ) , and set Y , with number of elements n ( Y ) , n ( X ∪ Y ) = n ( X ) + n ( Y ) − n ( X ∩ Y ) If A is a finite set, then its cardinality is n ( A ) = number of elements in A Calculation: Consider the provided table, New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100 The set C represents the set of successful authors, the set U represents the set of unsuccessful authors, the set N represents the new authors and the set E represents set of established authors. Reconstruct the table using symbols for sets as, New Authors Established Authors Total Successful n ( N ∩ C ) n ( E ∩ C ) n ( C ) Unsuccessful n ( N ∩ U ) n ( E ∩ U ) n ( U ) Total n ( N ) n ( E ) n ( S ) The set C ∩ N is the intersection of the sets C and N

7th Edition

ISBN: 9781337291262

Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

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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”.

Question

Chapter 6.2, Problem 37E

To determine

To prove: That n(C∪N)=n(C)+n(N)−n(C∩N), after describing C∩N and C∪N in words from the table given below:

New Authors

Established Authors

Total

Successful

5

25

30

Unsuccessful

15

55

70

Total

20

80

100

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Chapter 6.2, Problem 36E

Chapter 6.2, Problem 38E

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Chapter 6 Solutions

Finite Mathematics, Loose-leaf Version

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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To prove: That n ( C ∪ N ) = n ( C ) + n ( N ) − n ( C ∩ N ) , after describing C ∩ N and C ∪ N in words from the table given below: New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100

Solution Summary: The author analyzes the results of the survey of authors conducted by a fictitious publishing company.

Concept explainers

To prove: That n(C∪N)=n(C)+n(N)−n(C∩N), after describing C∩N and C∪N in words from the table given below:

New Authors

Established Authors

Total

Successful

5

25

30

Unsuccessful

15

55

70

Total

20

80

100

Want to see the full answer?

Chapter 6 Solutions

	New Authors	Established Authors	Total
Successful	5	25	30
Unsuccessful	15	55	70
Total	20	80	100

To prove: That n ( C ∪ N ) = n ( C ) + n ( N ) − n ( C ∩ N ) , after describing C ∩ N and C ∪ N in words from the table given below: New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100

Solution Summary: The author analyzes the results of the survey of authors conducted by a fictitious publishing company.

Concept explainers

To prove: That n(C∪N)=n(C)+n(N)−n(C∩N), after describing C∩N and C∪N in words from the table given below: New Authors Established Authors Total Successful 5 25 30 Unsuccessful 15 55 70 Total 20 80 100

Want to see the full answer?

Chapter 6 Solutions

To prove: That n(C∪N)=n(C)+n(N)−n(C∩N), after describing C∩N and C∪N in words from the table given below:

New Authors

Established Authors

Total

Successful

5

25

30

Unsuccessful

15

55

70

Total

20

80

100