Question

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 \(S \circ R\).

Short answer

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 \(\{ (2,1),(3,1),(3,2),(4,2)\} \).

Step-by-step solution

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 \(S \circ R\).

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.

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 \(\{ (2,1),(3,1),(3,2),(4,2)\} \).