   Chapter 7.4, Problem 20ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Give two examples of functions from Z to Z that one-to-one but not onto.

To determine

To find:

The two examples of function from to that are one-to-one but not onto.

Explanation

Given information:

One-to-one function but not onto.

Concept used:

Rational number can be written in the form of pq, where p,q and q0.

Calculation:

Example 1:

Define a function f: such that f(n)=2n

Then f is one-to-one but not onto.

Take

f(n1)=f(n2)2n1=2n2n1=n2

Therefore, f is one-to-one function.

Now ,

Let s=f(n) then

n=f1(s)s=2nn=s2

Then

f1(s)=s2f1(n)=n2

Therefore, f is not onto

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