   Chapter 8.2, Problem 16ES ### 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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# In 9-33, determine whether the given relation is reflexive symmetric, transitive, or none of these. Justify your answer.A is the “absolute value” relation on R: For all real numbers x and y , x , A , y   ⇔ | x | = | y | .

To determine

To justify whether the given relation is reflexive, symmetric, transitive, or none of these.

Explanation

Given information:

A is the “absolute value” relation on R:

For all real numbers x and y, x A y|x|=|y|.

Calculation:

Reflexive:

A is reflexive if it contains (x,x) for all xR.

|x|=|x| for all xR

Thus, we have

xAx,xR

It is reflexive

Symmetric:

The relation A on a set R Is symmetric if (b,a)A whenever (a,b)A.

For any arbitrary x,yR, |x|=|y| and by basic math |y|=|x|

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