To prove: That the function f : N → N defined by f ( m ) = { 2 m 3 if m ≡ 0 ( mod 3 ) 4 m − 1 3 if m ≡ 1 ( mod 3 ) 4 m + 1 3 if m ≡ 2 ( mod 3 ) is one-to-one and onto.

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Answer 1

Question

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

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Answer 2

Question

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

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Answer 3

Question

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

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Answer 4

Question

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

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Answer 5

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 6

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

Answer 7

Chapter 5.2, Problem 16E

(a)

To determine

To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

Answer 8

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 9

(b)

To determine

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 10

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 11

(c)

To determine

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 12

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 13

(d)

To determine

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 14

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 15

(e)

To determine

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 5.1 - True/False Questions The statement i=1n(2i1)=n2...Ch. 5.1 - Prob. 2TFQ Ch. 5.1 - Prob. 3TFQ Ch. 5.1 - Prob. 4TFQ Ch. 5.1 - Prob. 5TFQ Ch. 5.1 - Prob. 6TFQ Ch. 5.1 - Prob. 7TFQ Ch. 5.1 - Prob. 8TFQ Ch. 5.1 - Prob. 9TFQ Ch. 5.1 - Prob. 10TFQ

To prove: That the function f : N → N defined by f ( m ) = { 2 m 3 if m ≡ 0 ( mod 3 ) 4 m − 1 3 if m ≡ 1 ( mod 3 ) 4 m + 1 3 if m ≡ 2 ( mod 3 ) is one-to-one and onto.

Solution Summary: The author explains that the function f is one-to-one and onto if different elements of A have different images.

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To prove: That the function f:N→N defined by f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3) is one-to-one and onto.

The first ten terms of the sequence fn(1), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

The sequence fn(2), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

The sequence fn(4), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

Thefirst ten terms of the sequence fn(8), n≥1 where f(m)={2m3if m≡0(mod3)4m−13if m≡1(mod3)4m+13if m≡2(mod3).

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Chapter 5 Solutions