   Chapter 7.3, Problem 23ES ### 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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# Let f : W → Z , g : X → Y , and h : Y → Z be functions. Must h ∘ ( g ∘ f ) = ( h ∘ g ) ∘ f ? Prove or give a counterexample.

To determine

To check:

When f:WX,g:XY and h:YZ are three functions, then whether h(gf)=(hg)f must hold or not.

Explanation

Given information:

f:WX,g:XY and h:YZ are three functions.

Concept used:

(GF)(x)=G(F(x)).

Calculation:

Let W,X,Y and Z be any sets and the functions f:WX,g:XY and h:YZ.

The objective is to show that h(gf)=(hg)f.

Let wW

(h( gf))(w)=h[(gf)(w)

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