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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A biologist is investigating the effect of potential plant hormones by treating 20 stem segments. At the end of the observation period he computes the following length averages: Compound X = 1.18 Compound Y = 1.17 Based on these mean values he concludes that there are no treatment differences. 1) Are you satisfied with his conclusion? Why or why not? 2) If he asked you for help in analyzing these data, what statistical method would you suggest that he use to come to a meaningful conclusion about his data and why? 3) Are there any other questions you would ask him regarding his experiment, data collection, and analysis methods?

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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