a) Define what it means for a function from the set of

Chapter 2, Problem 9RQ

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QUESTION:

Problem 9RQ

a) Define what it means for a function from the set of positive integers to the set of positive integers to be one-to-one.

b) Define what it means for a function from the set of positive integers to the set of positive integers to be onto.

c) Give an example of a function from the set of positive integers to the set of positive integers that is both one-to-one and onto.

d) Give an example of a function from the set of positive integers to the set of positive integers that is one-to-one but not onto.

e) Give an example of a function from the set of positive integers to the set of positive integers that is not one-to-one but is onto.

f) Give an example of a function from the set of positive integers to the set of positive integers that is neither one-to-one nor onto.

 

Questions & Answers

QUESTION:

Problem 9RQ

a) Define what it means for a function from the set of positive integers to the set of positive integers to be one-to-one.

b) Define what it means for a function from the set of positive integers to the set of positive integers to be onto.

c) Give an example of a function from the set of positive integers to the set of positive integers that is both one-to-one and onto.

d) Give an example of a function from the set of positive integers to the set of positive integers that is one-to-one but not onto.

e) Give an example of a function from the set of positive integers to the set of positive integers that is not one-to-one but is onto.

f) Give an example of a function from the set of positive integers to the set of positive integers that is neither one-to-one nor onto.

 

ANSWER:

SOLUTION

a)Step 1

Let f is a function  from the set of positive integers to set of positive integers.

A function is said to be a one-one function,if every positive integer in the domain

is associated with one and only one positive integer in the co- domain.

b)

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