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Show that the set S is a countable set if there is a

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 33E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 33E

Show that the set S is a countable set if there is a function f from S to the positive integers such that f−1(j) is countable whenever j is a positive integer.

Step-by-Step Solution:

Step 1:

In this problem, we have to show that the set S is a countable set if there is a function f from s to the positive integers such that f - 1(j) is countable.

Step 2:

The definition of the countable set:

Now a set S is countable if there exists an injective function f: SN, (where N is the set of the natural number).

Therefore a countable set is a set with the same cardinality (number of elements) as some subset of the set of the natural numbers.

Step 3 of 3

Chapter 2.SE, Problem 33E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. This full solution covers the following key subjects: Countable, set, Positive, integers, Integer. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Show that the set S is a countable set if there is a function f from S to the positive integers such that f?1(j) is countable whenever j is a positive integer.” is broken down into a number of easy to follow steps, and 32 words. The full step-by-step solution to problem: 33E from chapter: 2.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. Since the solution to 33E from 2.SE chapter was answered, more than 248 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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