   Chapter 8.5, 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
1 views

# Let A = { a , b } . Describe all partial order relations on A.

To determine

To find:

All partial order relations on A.

Explanation

Given information:

Set A={a,b}.

Concept used:

If a relation is reflexive, antisymmetric and transitive then it is called partial order relation.

Calculation:

Consider a set A={a,b}.

Objective is to describe all partial order relations on a set A.

Partial order relation defined on set A={a,b} is R1={(a,a)(b,b)}.

Since (a,a) and (b,b) follows reflexive, antisymmetric and transitive by itself.

Second partial order relation is as follows.

R2={(a,a)(b,b)(a,b)}

The directed graph for R2 is as follows

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