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Give an example of a function from N to N that isa)

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 20E Chapter 2.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 20E

Give an example of a function from N to N that is

a) one-to-one but not onto.

b) onto but not one-to-one.

c) both onto and one-to-one (but different from the identity function).

d) neither one-to-one nor onto.

Step-by-Step Solution:

Step 1</p>

We have to find the example of a function from,  set of natural numbers to set of natural numbers that is,

Step 2</p>

a)One-one but not onto

Consider function

.

This function is one - one.

 

But this is not onto because zero is not in the image.

Step 3</p>

b)Onto but not one-one

 

Clearly

 Therefore the function is not one-one.

But this function is onto ,because for every element in the codomain has at least one preimage.

f(x+1) = x.

Step 4 of 5

Chapter 2.3, Problem 20E is Solved
Step 5 of 5

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Give an example of a function from N to N that isa)

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