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Q32E

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Discrete Mathematics and its Applications
Found in: Page 582
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

Let \(R\) the relation \(\{ (1,2),(1,3),(2,3),(2,4),(3,1)\} \) and \(S\) be the relation \(\{ (2,1),(3,1),(3,2),(4,2)\} \). Find \(S \circ R\).

The value of \(S^\circ R\) is \(\{ (1,1),(1,2),(2,1),(2,2)\} \) where \(R\) is the relation \(\{ (1,2),(1,3),(2,3),(2,4),(3,1)\} \) and \(S\) be the relation \(\{ (2,1),(3,1),(3,2),(4,2)\} \).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given

That \(R\) is the relation \(\{ (1,2),(1,3),(2,3),(2,4),(3,1)\} \) and \(S\) be the relation \(\{ (2,1),(3,1),(3,2),(4,2)\} \) and we need to find \(S \circ R\).

Step 2: The Concept of SoR in relation

If R is a relation from a set A to set B and S is a relation from B to a set C, then the relation SoR is from A to C.

Step 3: Determine the SoR

Consider the following relation as,

\(\begin{array}{l}R = \{ (1,2),(1,3),(2,3),(2,4),(3,1)\} \\S = \{ (2,1),(3,1),(3,2),(4,2)\} \end{array}\)

\(S^\circ R\) is found using the ordered pairs \(R\) and \(S\) where the second element of the ordered pair in _ agrees with the first element of the ordered pair in \(S\).

The computed ordered pairs are as shown below.

Hence the required composite function \(S \circ R\) is,

\(S \circ R = \{ (1,1),(1,2),(2,1),(2,2)\} {\rm{. }}\)

Conclusion:

Hence the value of \(S \circ R\) is \(\{ (1,1),(1,2),(2,1),(2,2)\} \) where \(R\) is the relation \(\{ (1,2),(1,3),(2,3),(2,4),(3,1)\} \) and \(S\) be the relation \(\{ (2,1),(3,1),(3,2),(4,2)\} \).

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