The verification of the law of conservation of flow at a , c , and d .

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Answer 1

Question

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

(b)

To determine

The value of the indicated flow.

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

(d)

To determine

Whether the given flow is maximum or not.

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

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Determine whether each function is an injection and determine whether each is a surjection.The notation Z_(n) refers to the set {0,1,2,...,n-1}. For example, Z_(4)={0,1,2,3}. f: Z_(6) -> Z_(6) defined by f(x)=x^(2)+4(mod6). g: Z_(5) -> Z_(5) defined by g(x)=x^(2)-11(mod5). h: Z*Z -> Z defined by h(x,y)=x+2y. j: R-{3} -> R defined by j(x)=(4x)/(x-3).

Determine whether each function is an injection and determine whether each is a surjection.

Let A = {a, b, c, d}, B = {a,b,c}, and C = {s, t, u,v}. Draw an arrow diagram of a function for each of the following descriptions. If no such function exists, briefly explain why. (a) A function f : AC whose range is the set C. (b) A function g: BC whose range is the set C. (c) A function g: BC that is injective. (d) A function j : A → C that is not bijective.

Answer 2

Question

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

(b)

To determine

The value of the indicated flow.

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

(d)

To determine

Whether the given flow is maximum or not.

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

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Answer 3

Question

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

(b)

To determine

The value of the indicated flow.

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

(d)

To determine

Whether the given flow is maximum or not.

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

Expert Solution & Answer

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Answer 4

Question

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

(b)

To determine

The value of the indicated flow.

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

(d)

To determine

Whether the given flow is maximum or not.

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

Expert Solution & Answer

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Answer 5

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

(b)

To determine

The value of the indicated flow.

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

(d)

To determine

Whether the given flow is maximum or not.

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

Answer 6

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

Answer 7

Chapter 14.1, Problem 3E

(a)

To determine

The verification of the law of conservation of flow at a, c, and d.

Answer 8

(b)

To determine

The value of the indicated flow.

Answer 9

(b)

To determine

The value of the indicated flow.

Answer 10

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

Answer 11

(c)

To determine

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

Answer 12

(d)

To determine

Whether the given flow is maximum or not.

Answer 13

(d)

To determine

Whether the given flow is maximum or not.

Answer 14

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

Answer 15

(e)

To determine

Illustration of Corollary 14.1.5 for S and T as in (c)

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

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

The verification of the law of conservation of flow at a , c , and d .

Solution Summary: The author explains the law of conservation of flow at a, c, and d.

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The verification of the law of conservation of flow at a, c, and d.

The value of the indicated flow.

The capacity of the (s,t) -cut defined by S={s,a,b,d} and T={c,e,f,t}

Whether the given flow is maximum or not.

Illustration of Corollary 14.1.5 for S and T as in (c)

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Chapter 14 Solutions