   Chapter 7.1, Problem 14ES ### 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
1 views

# Define functions H and K from R to R by the following formulas:For every x ∈ R , H ( x ) = ⌊ x ⌋ + 1 and K ( x ) = ⌈ x ⌉ . Does H = K? Explain.

To determine

Is h=k ? Explain.

Explanation

Given information:

Consider the functions h:J5J5 and k:J5J5.

Here J5={0,1,2,3,4}.

Define h(x) and k(x) for each x=J5 as follows.

h(x)=(x+3)3mod5k(x)=(x3+4x2+2x+2)mod5

The objective is to check whether h=k or not.

Concept used:

amod b = remainder

Calculation:

<
 x h(x)=(x+3)2mod5 k(x)=(x3+4x2+2x+2)mod5 0 h(0)=(3)2mod5=2 k(0)=(2)mod5=2

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