# Show that a subset of a countable set is also countable.

## Problem 16E Chapter 2.5

Discrete Mathematics and Its Applications | 7th Edition

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Problem 16E

Show that a subset of a countable set is also countable.

Step-by-Step Solution:

Step 1:

We have to prove that a subset of a countable set is also countable.

Step 2:

This statement can be proved by the theorem

Theorem: Every subset of a countable set is countable

Proof: Suppose x1 , x2, x3……… is a countable set A and B is any non-empty subset of A

If , for n, the element of xn belongs to B.

For each n

Let k(n) denote the number of elements  x1,, x2, x3…….xn which belong to the subset of B.

Then  0where B is countable

Step 3 of 3

##### ISBN: 9780073383095

The full step-by-step solution to problem: 16E from chapter: 2.5 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Since the solution to 16E from 2.5 chapter was answered, more than 249 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7th. This full solution covers the following key subjects: Countable, set, also, show, subset. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Show that a subset of a countable set is also countable.” is broken down into a number of easy to follow steps, and 11 words.

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