   Chapter 7.4, Problem 21ES ### 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
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# Give two examples of function from Z to Z that are onto but not one-to-one.

To determine

To find:

Two examples of functions from Z to Z which are onto but not one-to-one.

Explanation

Given information:

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

Calculation:

Define f: by f(n)=n/2.

This is onto but not one-to-one: it takes the value of every integer twice.

f is onto because the value n is attained on 2n, i.e.

f(2n)=n

f is not one-to-one because, for instance,

f(0)=f(1)=0.

Here x is the floor function, which rounds down to the nearest smaller integer

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