   Chapter 6.4, Problem 29ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Use a technique similar to that used to derive Russell’s paradox to prove that for any set ???

To determine

Use a technique similar to that used to derive Russell’s paradox to prove that for any set A.

P(A)A.

Explanation

Given information:

Concept used:

If S={A|A is a set and AA} is the set of all sets that are not elements of themselves, then neither SS nor SS.

Calculation:

If S={A|A is a set and AA} is the set of all sets that are not elements of themselves, then neither SS nor SS.

Use the above technique to prove that P(A)A

Suppose there exists a set A that contains its power set.

That is, P(A)A

Consider the set B={xA|xx}. Then, B is contained in A, and so BP(A)

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