Chapter 8.5, Problem 32ES

### 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 , b ) , ( a , d ) , ( c , d ) , ( b , d ) , ( c , d ) , ( c , a ) } . Is R total order on A? Justify your answer.

To determine

To check:

Whether R is a toal order relation on A where A={a,b,c,d},

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

Explanation

Given information:

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

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

Concept used:

R is reflexive, antisymmetric and transitive so it is a partial order relation.

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,b),(a,d),(b,a),(b,d),(c,d),(c,a)}

Firstly verify the properties reflexivity antisymmetric and transitivity for the given relation R to check the partial order relation.

The set above R contains the ordered pairs (a,a),(b,b)(c,c),(d,d) which show that the relation R is reflexive.

Observe the two sets of the ordered pairs

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