   Chapter 7.4, Problem 29ES ### 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

# Prove that a union of any two countably infinite sets is countably infinite.

To determine

To prove:

A union of any two countably infinite sets is countably infinite.

Explanation

Given information:

Disjoint union of finite set

Concept used:

X be an infinite set.

Calculation:

Let A be any countable infinite set.

Then there exist one-to-one, onto correspondence f:Z+A.

Let A and B be countable infinite set.

Case1.

To prove AB is countable infinite if AB=Φ.

Define a function h:Z+AB as follows: for all integer n1.

h(n)={f(n/2)                if n is evenf(( n+1)/2)         if n is odd

The above function is one-to-one and onto.

Therefore, there exists one-to-one correspondence h:Z+AB.

Hence, AB is countable infinite because set A and B is countable infinite.

Therefore, the result stated in the question has been proved.

Case 2

### 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 