   Chapter 7.3, Problem 7ES ### 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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# Define L : Z → Z and M : Z → Z by the rules L ( a ) = a 2 and M ( a ) = a   m o d   5 for each integer a.a. Find ( L ∘ M ) ( 12 ) ,   ( M ∘ L ) ( 12 ) ,   ( L ∘ M ) ( 9 ) , and ( M ∘ L ) ( 9 ) .b. Is L ∘ M = M ∘ L ?

To determine

(a)

To find:

(LM)(12), (ML)(12), (LM)(9) and (ML)(9).

Explanation

Given information:

The functions L: and M: are defined by the rules:

L(a)=a2 and M(a)=amod5, for all a.

Concept used:

fg(x)=f{g(x)}

Calculation:

(LM)(12)=L{M(12)}=L(12mod5)=L(2)=22=4

(ML)(12)=M{L(12)}=M(144)=144

To determine

(b)

To check:

Whether LM equals ML.

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