   Chapter 7.1, Problem 41ES ### 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. If A ⊆ B then F ( A ) ⊆ F ( B ) .

To determine

To show:

If AB then F(A)F(B).

Explanation

Given information:

AB

Concept used:

f(A)f(B) only if for each element yf(A), it belongs to f(B) also.

Calculation:

It is given that y=f(x) for some xA.

So, yf(A).

But A is a subset of B, AB.

Therefore, if xA then x belongs to B also, xB.

The definition of a function states a property according to which no element of the domain set of

the function can have more than one image in the co-domain set

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