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This exercise presents Russell’s paradox. Let S be the set

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

Solution for problem 46E Chapter 2.1

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 46E

This exercise presents Russell’s paradox. Let S be the set that contains a set x if the set x does not belong to itself, so that S = {x | x ∉ .x}.

a) Show the assumption that S is a member of S leads to a contradiction.

b) Show the assumption that S is not a member of S leads to a contradiction.

By parts (a) and (b) it follows that the set S cannot be defined as it was. This paradox can be avoided by restricting the types of elements that sets can have.

Step-by-Step Solution:
Step 1 of 3

Step-1:

a)In this problem we need to show the assumption that S is a member of S leads to a contradiction.

Russell’s paradox: Let S be the set that contains a set x if the set does not belongs to itself , so that .

If , then by using the Russell’s paradox condition for S we conclude that , a contradiction.

Step-2:

b)In this problem...

Step 2 of 3

Chapter 2.1, Problem 46E is Solved
Step 3 of 3

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

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 46E from chapter: 2.1 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Since the solution to 46E from 2.1 chapter was answered, more than 412 students have viewed the full step-by-step answer. This full solution covers the following key subjects: set, paradox, assumption, show, member. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “This exercise presents Russell’s paradox. Let S be the set that contains a set x if the set x does not belong to itself, so that S = {x | x ? .x}.a) Show the assumption that S is a member of S leads to a contradiction.________________b) Show the assumption that S is not a member of S leads to a contradiction.By parts (a) and (b) it follows that the set S cannot be defined as it was. This paradox can be avoided by restricting the types of elements that sets can have.” is broken down into a number of easy to follow steps, and 93 words.

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