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Expert-verified Found in: Page 582 ### Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095 # 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 $$\{ (2,1),(3,1),(3,2),(4,2)\}$$.

See the step by step solution

## 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 $$\{ (2,1),(3,1),(3,2),(4,2)\}$$. ### Want to see more solutions like these? 