   Chapter 7.1, Problem 44ES ### 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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# In 41-49 let X and Y be sets, let A and B be any subsets of X, and let C and D be any subsets of Y. Determine which of the properties are true for every fubnction F from X to Y of the properties are ture for every function F from X to Y and which are false for at lest for at lest one functions F from X to Y. Justify your answer. For all subsets A and B of X, F ( A − B ) = F ( A ) − F ( B ) .

To determine

To check the given property whether it is true for all functions F from X to Y or it is false for at least one function F from X to Y.

Explanation

Given information:

A and B are any two subsets of a set X.

Calculation:

Objective is to determine the property, F(AB)=F(A)F(B) whether it is true or not.

For this, consider two subsets A={1,2,3} and B={1} of X.

Then, AB={2,3}.

Now, define a function F:XY such that F(x)=k, for all x belongs to X.

Here, k is any fixed constant.

Then,

F(AB)=F({2,3})={k}

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