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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

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.

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:

Let F be a function from X to Y.

Take yF(AB).

Since yF(AB), so by definition of image of a set, we have y=F(x) for some xAB.

This implies that y=F(x) for some xA and xB.

So, we have y=F(x) for some xA and y=F(x) for some xB

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