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Explain w by the set A is countable if and only if |A|

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

Solution for problem 13E Chapter 2.5

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 13E

Explain w by the set A is countable if and only if |A| ≤ |Z+|.

Step-by-Step Solution:

We need to show that a set A is countable if and only if

Step 1</p>

By definition, A set is called countable if it is finite or it has the same cardinality as the set of positive integers.

Step 2</p>

By definition of cardinality , if there is injection (one to one relation) from A to B then the cardinality of A is less than or equal to the cardinality of B.

Therefore we can write it as

Step 3</p>

There is a proposition stating that if  be an injection .then if B is countable then  A is also countable.

Step 4 of 6

Chapter 2.5, Problem 13E is Solved
Step 5 of 6

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Explain w by the set A is countable if and only if |A|

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