   Chapter 8.2, 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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# In 1-8, a number of relations are defined on the et A={0,1,2,3}. For each relation: Drae the directed graph. Determine whethrer the relation is reflexive. Determine whether the relation is symmetric. Determine whether the realtion is transitive. Give a counter example in each case in which the relation does not satisfy one of the properties. R 1 = { ( 0 , 0 ) , ( 0 , 1 ) , ( 0 , 3 ) , ( 1 , 1 ) , ( 2 , 3 ) , ( 3 , 3 ) }

To determine

(a)

Draw a directed graph for the given relation.

Explanation

Given information:

The relation R1 is defined on the set A={0,1,2,3} .

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

Calculation:

A ={0, 1, 2, 3}.

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

Directed graph:A Directed graph of ordered pair (x,y) such that xy must contain an arrow from x to y and should satisfy xRy

To determine

(b)

To justify whether the given relation is reflexive or not.

To determine

(c)

To justify whether the given relation is symmetric or not.

To determine

(d)

To justify whether the given relation is transitive or not.

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