Explanation Given Information: The provided sets are A = { Dirk, Johan, Frans, Sarie } , B = { Frans, Sarie, Tina, Klaas, Henrika } and C = { Hans, Frans } . The equation is n ( A ∪ B ) = n ( A ) + n ( B ) − n ( A ∩ B ) . Formula used: If A is a finite set, then its cardinality is n ( A ) = number of elements in A Proof: Consider the set, A = { Dirk, Johan, Frans, Sarie } There are 4 terms in the set A . So, n ( A ) = 4 Consider the set, B = { Frans, Sarie, Tina, Klaas, Henrika } There are 5 terms in the set B . So, n ( B ) = 5 The intersection of sets A and B will contain all the elements that are common in both the sets A and B . This is represented by, A ∩ B = { Frans, Sarie } There are 2 terms in the set A ∩ B

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 6.2, Problem 7E

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To prove: The equation n(A∪B)=n(A)+n(B)−n(A∩B), for the provided sets A, B and C.

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Chapter 6.2, Problem 6E

Chapter 6.2, Problem 8E

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To prove: The equation n ( A ∪ B ) = n ( A ) + n ( B ) − n ( A ∩ B ) , for the provided sets A , B and C .

Solution Summary: The author explains the equation for the provided sets A, B, and C.

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To prove: The equation n(A∪B)=n(A)+n(B)−n(A∩B), for the provided sets A, B and C.

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