   Chapter 7.3, 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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# True or False? Given any set X and given any function f : X → X , g : X → X , and h : X → X , if h is one-to-one and h ∘ f = h ∘ g , then f = g . Justify your answer.

To determine

To check:

Whether the given statement, “Given any set X and given any functions f:XX,g:XX and h:XX if h is one-to-one and ho f=ho g then f=g ” is true or false.

Explanation

Given information:

h:one-to-one

ho f=ho g.

Concept used:

A function is said to be one-to-one function if the distinct elements in domain must be mapped with distinct elements in co-domain.

Calculation:

The given statement is true.

Since h is a one-to-one function from X to X.

So for every x,y in X ,

h(x)=h(y)x=y

Also, consider that ho f=ho g.

Therefore (ho f)(a)=(ho g)(a), for all a in X

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