   Chapter 8.5, Problem 1ES ### 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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# Each of the following is a relation on { 0 , 1 , 2 , 3 } Draw directed graphs for each relation, and indicate which relations are antisymmetric. R 1 = { ( 0 , 0 ) , ( 0 , 2 ) , ( 1 , 0 ) , ( 2 , 2 ) ( 3 , 0 ) , ( 3 , 1 ) } R 2 = { ( 0 , 0 ) , ( 0 , 2 ) , ( 1 , 0 ) , ( 2 , 2 ) ( 3 , 0 ) , ( 3 , 1 ) }

To determine

(a)

To draw:

The directed graph for given relation and also check whether the given relation is antisymmetric.

Explanation

Given information:

R1={(0,0),(0,2),(1,0),(1,3),(2,2),(3,0),(3,1)}.

Concept used:

Directed graph.

Calculation:

Let R1={(0,0),(0,2),(1,0),(1,3),(2,2),(3,0),(3,1)} be a relation on {0,1,2,3}.

It needs to draw a directed graph for the relation R1 and then determine whether it is antisymmetric or not

To determine

(b)

To draw:

The directed graph of

R2={(0,1),(0,2),(1,1),(1,2),(1,3),(2,2),(3,2)}

and also check whether the given relation is antisymmetric.

To determine

(c)

To draw:

The directed graph of R3={(0,0),(0,3),(1,0),(1,3),(2,2),(3,3),(3,2)}

and also check whether the given relation is antisymmetric.

To determine

(d)

To draw:

The directed graph of R4={(0,0),(1,0),(1,2),(1,3),(2,0),(2,1),(3,2),(3,0)} and also check whether the given relation is antisymmetric.

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