   Chapter 7.4, Problem 31ES ### 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

# Use the results of exercise 28 and 29 to prove that a union of any two countable sets is countable.

To determine

To prove:

A union of any two countable sets is countable.

Explanation

Given information:

1 A disjoint union of any finite set and any countably infinite set is countably infinite.

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

Concept used:

Union of any two countably infinite sets is countably infinite.

Calculation:

Let A,B be two countable sets. Use the following cases to prove the given theorem.

Case 1:

Suppose both A,B are finite.

Then, AB=A(BA)

Since A and BA are finite and disjoint therefore, AB=A(BA) is finite.

Hence AB is countable

### 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 