To prove: If f : Z 4 → Z 8 .then f is one-to-one but not onto Z 8 .

Question

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Answer 1

Question

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

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Answer 2

Question

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

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Answer 3

Question

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

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Answer 4

Question

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

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Answer 5

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

Answer 6

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

Answer 7

Chapter 4.3, Problem 12E

(a)

To determine

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

Answer 8

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

Answer 9

(b)

To determine

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

Answer 10

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

Answer 11

(c)

To determine

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

Answer 12

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

Answer 13

(d)

To determine

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 4.1 - Find two upper bounds (if any exits) for each of...Ch. 4.1 - Assign a grade of A (correct), C (partially...Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Let A and B be subsets of . Prove that if A is...Ch. 4.1 - Let x be an upper bound for A. Prove that if xy,...Ch. 4.1 - Let A. Prove that if A is bounded above, then Ac...Ch. 4.1 - Give an example of a set A for which both A and Ac...Ch. 4.1 - Let A. Prove that if sup(A) exists, then it is...Ch. 4.1 - Formulate and prove a characterization of greatest...

To prove: If f : Z 4 → Z 8 .then f is one-to-one but not onto Z 8 .

Solution Summary: The author analyzes how f is one-to-one, but not onto N.

Concept explainers

To prove:If f:Z4→Z8 .then f is one-to-one but not onto Z8 .

To prove: If f:Z4→Z2 .then f is onto Z2 but not one-to-one.

To prove: If f:Z6→Z6 .then f is onto and one-to-one Z6

To prove: If f:Z4→Z4 then f is not one to one and not onto Z4 .

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Chapter 4 Solutions