BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Solutions

Chapter
Section
BuyFindarrow_forward

Discrete Mathematics With Applicat...

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

a. Define f : Z Z by the rule f ( n ) = 2 n , for every integer n.
(i) Is f one-to-one? Prove or give a counterexample.
(ii) Is f onto? Prove or give a counterexample.
b. Let 2Z denote the set of all even integers. That is, 2 Z = { n Z | n = 2 k , for some integer k } . Define h : Z 2 Z by the rule h ( n ) = 2 n , for each integer n. Is h onto? Prove or give a counterexample.

To determine

(a)

To prove f is one-to-one and onto otherwise give counterexample.

Explanation

Given information:

Define f:ZZ by the rule, f(n)=2n for all integers n.

Calculation:

Let us suppose x,yZ and assume that f(x)=f(y) and now prove x=y

So from the definition of f(n), the expression can be written as follows-

2x=2yx=y{dividing by 2 on both sides}

Thus,

To determine

(b)

To define h:Z2Z by the rule, h(n)=2n for all integers n and also define whether the function is onto or not.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started
Sect-7.1 P-2ESSect-7.1 P-3ESSect-7.1 P-4ESSect-7.1 P-5ESSect-7.1 P-6ESSect-7.1 P-7ESSect-7.1 P-8ESSect-7.1 P-9ESSect-7.1 P-10ESSect-7.1 P-11ESSect-7.1 P-12ESSect-7.1 P-13ESSect-7.1 P-14ESSect-7.1 P-15ESSect-7.1 P-16ESSect-7.1 P-17ESSect-7.1 P-18ESSect-7.1 P-19ESSect-7.1 P-20ESSect-7.1 P-21ESSect-7.1 P-22ESSect-7.1 P-23ESSect-7.1 P-24ESSect-7.1 P-25ESSect-7.1 P-26ESSect-7.1 P-27ESSect-7.1 P-28ESSect-7.1 P-29ESSect-7.1 P-30ESSect-7.1 P-31ESSect-7.1 P-32ESSect-7.1 P-33ESSect-7.1 P-34ESSect-7.1 P-35ESSect-7.1 P-36ESSect-7.1 P-37ESSect-7.1 P-38ESSect-7.1 P-39ESSect-7.1 P-40ESSect-7.1 P-41ESSect-7.1 P-42ESSect-7.1 P-43ESSect-7.1 P-44ESSect-7.1 P-45ESSect-7.1 P-46ESSect-7.1 P-47ESSect-7.1 P-48ESSect-7.1 P-49ESSect-7.1 P-50ESSect-7.1 P-51ESSect-7.1 P-52ESSect-7.1 P-53ESSect-7.2 P-1TYSect-7.2 P-2TYSect-7.2 P-3TYSect-7.2 P-4TYSect-7.2 P-5TYSect-7.2 P-6TYSect-7.2 P-7TYSect-7.2 P-8TYSect-7.2 P-9TYSect-7.2 P-10TYSect-7.2 P-11TYSect-7.2 P-1ESSect-7.2 P-2ESSect-7.2 P-3ESSect-7.2 P-4ESSect-7.2 P-5ESSect-7.2 P-6ESSect-7.2 P-7ESSect-7.2 P-8ESSect-7.2 P-9ESSect-7.2 P-10ESSect-7.2 P-11ESSect-7.2 P-12ESSect-7.2 P-13ESSect-7.2 P-14ESSect-7.2 P-15ESSect-7.2 P-16ESSect-7.2 P-17ESSect-7.2 P-18ESSect-7.2 P-19ESSect-7.2 P-20ESSect-7.2 P-21ESSect-7.2 P-22ESSect-7.2 P-23ESSect-7.2 P-24ESSect-7.2 P-25ESSect-7.2 P-26ESSect-7.2 P-27ESSect-7.2 P-28ESSect-7.2 P-29ESSect-7.2 P-30ESSect-7.2 P-31ESSect-7.2 P-32ESSect-7.2 P-33ESSect-7.2 P-34ESSect-7.2 P-35ESSect-7.2 P-36ESSect-7.2 P-37ESSect-7.2 P-38ESSect-7.2 P-39ESSect-7.2 P-40ESSect-7.2 P-41ESSect-7.2 P-42ESSect-7.2 P-43ESSect-7.2 P-44ESSect-7.2 P-45ESSect-7.2 P-46ESSect-7.2 P-47ESSect-7.2 P-48ESSect-7.2 P-49ESSect-7.2 P-50ESSect-7.2 P-51ESSect-7.2 P-52ESSect-7.2 P-53ESSect-7.2 P-54ESSect-7.2 P-55ESSect-7.2 P-56ESSect-7.2 P-57ESSect-7.2 P-58ESSect-7.3 P-1TYSect-7.3 P-2TYSect-7.3 P-3TYSect-7.3 P-4TYSect-7.3 P-5TYSect-7.3 P-1ESSect-7.3 P-2ESSect-7.3 P-3ESSect-7.3 P-4ESSect-7.3 P-5ESSect-7.3 P-6ESSect-7.3 P-7ESSect-7.3 P-8ESSect-7.3 P-9ESSect-7.3 P-10ESSect-7.3 P-11ESSect-7.3 P-12ESSect-7.3 P-13ESSect-7.3 P-14ESSect-7.3 P-15ESSect-7.3 P-16ESSect-7.3 P-17ESSect-7.3 P-18ESSect-7.3 P-19ESSect-7.3 P-20ESSect-7.3 P-21ESSect-7.3 P-22ESSect-7.3 P-23ESSect-7.3 P-24ESSect-7.3 P-25ESSect-7.3 P-26ESSect-7.3 P-27ESSect-7.3 P-28ESSect-7.3 P-29ESSect-7.3 P-30ESSect-7.4 P-1TYSect-7.4 P-2TYSect-7.4 P-3TYSect-7.4 P-4TYSect-7.4 P-5TYSect-7.4 P-6TYSect-7.4 P-7TYSect-7.4 P-8TYSect-7.4 P-9TYSect-7.4 P-1ESSect-7.4 P-2ESSect-7.4 P-3ESSect-7.4 P-4ESSect-7.4 P-5ESSect-7.4 P-6ESSect-7.4 P-7ESSect-7.4 P-8ESSect-7.4 P-9ESSect-7.4 P-10ESSect-7.4 P-11ESSect-7.4 P-12ESSect-7.4 P-13ESSect-7.4 P-14ESSect-7.4 P-15ESSect-7.4 P-16ESSect-7.4 P-17ESSect-7.4 P-18ESSect-7.4 P-19ESSect-7.4 P-20ESSect-7.4 P-21ESSect-7.4 P-22ESSect-7.4 P-23ESSect-7.4 P-24ESSect-7.4 P-25ESSect-7.4 P-26ESSect-7.4 P-27ESSect-7.4 P-28ESSect-7.4 P-29ESSect-7.4 P-30ESSect-7.4 P-31ESSect-7.4 P-32ESSect-7.4 P-33ESSect-7.4 P-34ESSect-7.4 P-35ESSect-7.4 P-36ESSect-7.4 P-37ESSect-7.4 P-38ES