   Chapter 8.5, Problem 9ES ### 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 a relation R on R, the set of all real numbers as follows: For every x , y ∈ R , x R y   ⇔ x 2 ≤ y 2 . Is R a partial order relation? Prove or give a counterexample.

To determine

To check:

Whether R is a partial order relation or not.

Explanation

Given information:

Consider a relation R on the real number set as follows.

xRyx2y2. For all x,y.

Concept used:

A relation that is reflexive, antisymmetric, and transitive is called a partial order.

Calculation:

Objective is to identify whether the relation is partial order relation or not.

A relation R on the set A is a partial order relation if R is reflexive, antisymmetric, and transitive.

A relation R on the set A is antisymmetric if for all a and b in A, if aRb and bRa then a=b.

Here, the relation R defined on a real number set xRyx2y2 is not a partial order relation since R is not antisymmetric.

Counterexample

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