Chapter 8.5, Problem 31ES

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Chapter
Section

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let A = { a , b , c , d } , and let R be the relation R = { ( a , a ) , ( b , b ) , ( c , c ) , ( d , d ) , ( c , a ) , ( a , d ) , ( c , d ) , ( b , c ) , ( b , d ) , ( b , a ) } . Is R total order on A? Justify your answer.

To determine

To check:

Whether the relation R is a total order relation on A.

Explanation

Given information:

Let A={a,b,c,d} and let R be the relation.

R={(a,a),(b,b)(c,c),(d,d),(c,a),(a,d),(c,d),(b,c),(b,d),(b,a)}.

Concept used:

R is reflexive, antisymmetric and transitive so it is a partial order relation otherwise it will be a total order relation.

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

Calculation:

The relation R on the set {a,b,c,d} is defined as follows.

R={(a,a),(b,b)(c,c),(d,d),(c,a),(a,d

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