   Chapter 7.3, Problem 25ES ### 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 functions f : X → X , g : X → X , and h : X → X , if h is one-to-one and f ∘ h = g ∘ h , 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 fo h=go h then f=g ” is true or false.

Explanation

Given information:

f:XX,g:XX and h:XX be three functions.

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:

Let X be any set and the functions f:XX,g:XX and h:XX.

Consider the statement,

Any set X and any functions f:XX,g:XX and h:XX if h is one-to-one and fo h=go h then f=g.

The objective is to identify whether it is true or false.

This statement is false.

Find the below counterexample:

Let X be the natural number set N.

Define the function f:NN by,

f(x)={x, if xis even1,if xis odd

Define the function g:NN by,

g(x)={x, if xis even3,if xis odd

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