   Chapter 7.2, Problem 9ES ### 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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# Let X = { 1 , 2 , 3 } , Y = { 1 , 2 , 3 , 4 } , and Z= { 1 , 2 } Define a function f : X → Z that is onto but not one-to-one. Define a function g : X → Z that is onto but not one-to-one. Define a function h : X → X that is neither one-to-one nor onto. Define a function k : X → X that is one-to-one and onto but is not the identity functions on X.

To determine

(a)

To find:

A function f:XY which is one-to-one but not onto.

Explanation

Given information:

Let X={1,2,3},Y={1,2,3,4} and Z={1,2}

To determine

(b)

To find:

A function g:XZ which is onto but not one-to-one.

To determine

(c)

To find:

A function h:XX which is neither one-to-one nor onto.

To determine

(d)

To find:

A function k:XX which is one-to-one and onto but is not the identity function on X.

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