   Chapter 8.5, Problem 8ES ### 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 Z, the set of all integers as follows: For every m , n ∈ Z , m R n ⇔ m + n   is even . 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 the relation R on the set of integers ,

For all m,n,mRnm+n is even.

Concept used:

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

Calculation:

Objective is to identify whether R is a partial order relation or not

If R is reflexive, antisymmetric and transitive, then R is called a partial order relation on a set A.

For all a,bA, a relation R is antisymmetric if aRband bRa then a=b

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