To prove: f is one-to-one if and only if f is onto.

Question

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Answer 1

Question

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

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Answer 2

Question

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

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Answer 3

Question

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

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Answer 4

Question

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

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Answer 5

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

Answer 6

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

Answer 7

Chapter 3.1, Problem 32E

(a)

To determine

To prove: f is one-to-one if and only if f is onto.

Answer 8

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

Answer 9

(b)

To determine

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

Answer 10

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

Answer 11

(c)

To determine

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 3.1 - True/False Questions A function from a set A to a...Ch. 3.1 - Prob. 2TFQ Ch. 3.1 - Prob. 3TFQ Ch. 3.1 - Prob. 4TFQ Ch. 3.1 - Prob. 5TFQ Ch. 3.1 - True/False Questions Define f:ZZ by f(x)=x+2. Then...Ch. 3.1 - Prob. 7TFQ Ch. 3.1 - Prob. 8TFQ Ch. 3.1 - Prob. 9TFQ Ch. 3.1 - Prob. 10TFQ

To prove: f is one-to-one if and only if f is onto.

Solution Summary: The author explains how to prove that f is one-to-one if A and B contain the same (finite) number of elements.

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To prove: f is one-to-one if and only if f is onto.

An example of a one-to-one function N→N that is not onto. Also find whether this contradict (a).

An example of an onto function N→N that is not one-to-one. Also find whether this contradict (a).

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Chapter 3 Solutions