The reason if a set S and n subsets A 1 , A 2 ....... A n of S, it is possible to select distinct elements s 1 , s 2 , .......... s n of S such that s 1 ∈ A 1 , s 2 ∈ A 2 , .... s n ∈ A n if and only if, for each subset X of { 1 , 2 , ........ , n } , the number of elements is U x ∈ X A x at least | X | .

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Answer 1

Question

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

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Answer 2

Question

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

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Answer 3

Question

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

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Answer 4

Question

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

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Answer 5

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

Answer 6

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

Answer 7

Chapter 14.4, Problem 7E

(a)

To determine

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

Answer 8

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

Answer 9

(b)

To determine

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

Answer 10

Expert Solution & Answer

Answer 11

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Answer 12

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Answer 13

Ch. 14.1 - 1. This directed network illustrates a valid -...Ch. 14.1 - Prob. 2TFQ Ch. 14.1 - Prob. 3TFQ Ch. 14.1 - Prob. 4TFQ Ch. 14.1 - Prob. 5TFQ Ch. 14.1 - Prob. 6TFQ Ch. 14.1 - Prob. 7TFQ Ch. 14.1 - Prob. 8TFQ Ch. 14.1 - Prob. 9TFQ Ch. 14.1 - Prob. 10TFQ

Solution Summary: The author explains how to construct a bipartite graph with vertex sets V_1 and

Concept explainers

The reason if a set S and n subsets A1,A2.......An of S, it is possible to select distinct elements s1,s2,..........sn of S such that s1∈A1,s2∈A2,....sn∈An if and only if, for each subset X of {1,2,........,n}, the number of elements is Ux∈XAx at least |X|.

To prove: It is always possible to select 13 cards, one of each of the 13 denominations

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Chapter 14 Solutions