   Chapter 7.1, Problem 13ES ### 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 J s = { 0 , 1 , 2 , 3 , 4 } , and define functions f : J s → J s and g : J s → J S as follows: For each x ∈ J s . f ( x ) = ( x + 4 ) 4 mod   5   and g ( x ) = ( x 2 + 3 x + 1 )   mod   5. Is f = g ? Exapain.

To determine

To prove:

Is f=g Explain.

Explanation

Given information:

Let J5={0,1,2,3,4} and define functions fJ5J5 and J5J5 as follows. For each xJ5, f(x)=(x+4)2 mod 5 and g(x)=(x2+3x+1)mod5.

Concept used:

amod b = remainder

Calculation:

Consider the function f:J5J5 and g:J5J5 for all xJ5.

Function f(x) and g(x) is defined as.

f(x)=(x+4)2mod5

And

g(x)=(x2+3x+1)mod5

Consider J5={0,1,2,3,4}

To prove f=g

To compute f(x) and g(x) for all xJ5 as shown below.

 x f(x)=(x+4)2mod5 g(x)=(x2+3x+1)mod5 0 f(0)=(4)2mod5

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