Show that a subset of a countable set is also countable.
We have to prove that a subset of a countable set is also countable.
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
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
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 286 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: 7. 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.