   Chapter 6.4, Problem 24ES ### 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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# Can there exist a cimputer program that has as output a list of all the computer programs that do not list themselves in their oputput? Explain your answer.

To determine

Can there exist a computer program that has as output a list of all the computer programs that do not list themselves in their output? Explain your answer

Explanation

Given information:

Existence of computer program

Concept used:

In general, in the implication, A B(if A then B), A stands for the antecedent, and, B stands for tile consequent.

Calculation:

Consider the following set of all the computer programs that do not list themselves in their output:

S={A|A is a computer programme and AA}.

It is required to check whether there is a computer programme that has list S as output.

Use Russell’s paradox which s stated as follows:

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

Suppose there exists a computer programme P that had the list S as output.

P={xA|xx}

If PP then P satisfies the defining property for P and hence PP

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