   Chapter 8.2, Problem 52ES ### 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 51—53, R, S, and T are relations defined on A = { 0 ,   1 ,   2 ,   3 } .52. Let S = { ( 0 ,  0 ) ,     ( 0 ,  3 ) ,   ( 1 ,  0 ) ,   ( 1 ,  2 ) ,   ( 2 ,  0 ) ,   ( 3 ,   2 ) } .Find S t , the transitive closure of S.

To determine

The set St, transitive closure of S.

Explanation

Given information:

S is a relation defined on A={0,1,2,3}.

Let S={(0,0),(0,3),(1,0),(1,2),(2,0),(3,2)}.

Calculation:

A= {0,1,2,3}

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

The transitive closure of S needs to contain all ordered pairs in the relation S :

{(0,0),(0,3),(1,0),(1,2),(2,0),(3,2)}St

The transitive closure of S is the smallest relation that contains S and that is transitive. Let us next determine which pairs to add using the transitive property.

(0,0)St and (0,3)St(0,3)St(0,3)St and (3,2)St(0,2)St(1,0)St and (0,0)St(1,0)St

(1,0)St and (0,3)St(1,3)St(1,2)St and (2,0)St(1,0)St(2,0)St and (0,0)St(2,0)St(2,0)St and (0,3)St(2<

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