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Math
Discrete Mathematics With Applications5th Edition

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Chapter 7.4, Problem 37ES
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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Solutions

Chapter
Section
Problem 1TY
Problem 2TY
Problem 3TY
Problem 4TY
Problem 5TY
Problem 6TY
Problem 7TY
Problem 8TY
Problem 9TY
Problem 1ES
Problem 2ES
Problem 3ES
Problem 4ES
Problem 5ES
Problem 6ES
Problem 7ES
Problem 8ES
Problem 9ES
Problem 10ES
Problem 11ES
Problem 12ES
Problem 13ES
Problem 14ES
Problem 15ES
Problem 16ES
Problem 17ES
Problem 18ES
Problem 19ES
Problem 20ES
Problem 21ES
Problem 22ES
Problem 23ES
Problem 24ES
Problem 25ES
Problem 26ES
Problem 27ES
Problem 28ES
Problem 29ES
Problem 30ES
Problem 31ES
Problem 32ES
Problem 33ES
Problem 34ES
Problem 35ES
Problem 36ES
Problem 37ES
Problem 38ES
BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Prove that if A and B are any countably infinite set, then A × B is countably infinite.

To determine

To prove:

If A and B are any countably infinite sets, then A×B is countably infinite.

Explanation

Given information:

A and B are any countably infinite sets.

Concept used:

A function is said to be one-to-one function if the distinct elements in domain must be mapped with distinct elements in co-domain.

A function is onto function if each element in co-domain is mapped with atleast one element in domain.

Proof:

Let us consider set A and B as any countably infinite sets.

Since, A is countably infinite set the elements of the set are listed as shown below.

A:a1,a2,a3,........

Similarly, the elements of the set B are listed as shown below

B:b1,b2,b3,........

Now, let us consider the cartesian product of the two set A×B.

The elements of A×B are represented in a grid form as shown below.

(a1,b1)  (a1,b2)  (a1,b3)  ⋯(a2,b1)  (a2,b2)  (a2,b3)  ⋯(a3,b1) (a3,b2)  (a3,b3)  ⋯    ⋮            ⋮           ⋮

Now, define a function F from Z+ to A×B by starting to count at (a1,b1) and moving horizontally, diagonally and vertically as shown below

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Chapter 7.4,
Problem 36ES
Chapter 7.4,
Problem 38ES
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Chapter 7 Solutions

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Sect-7.1 P-1TYSect-7.1 P-2TYSect-7.1 P-3TYSect-7.1 P-4TYSect-7.1 P-5TYSect-7.1 P-6TYSect-7.1 P-7TYSect-7.1 P-8TYSect-7.1 P-9TYSect-7.1 P-1ES
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
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