Question

Let$R=\left\{(1,3),(2,2),(3,2)\right\}\text{and}S=\left\{(2,1),(3,2),(2,3)\right\}$ be two relations on set $A=\left\{1,2,3\right\}$. Then $SoR=$

• A. $\left\{(1,3),(2,2),(3,2),(2,1),(2,3)\right\}$
• B. $\left\{(3,2),(1,3)\right\}$
• C. $\left\{(2,3),(3,2),(2,2)\right\}$
• D. $\left\{(3,2),(2,1),(2,3)\right\}$

Answer 1

The correct option is D

$\left\{(3,2),(2,1),(2,3)\right\}$

Explanation for the correct Option.

Finding the value of $SoR=$

Given: $R=\left\{(1,3),(2,2),(3,2)\right\}\text{and}S=\left\{(2,1),(3,2),(2,3)\right\}$

$$\begin{gathered} R\left(1\right)=3 \\ R\left(2\right)=2 \\ R\left(3\right)=2 \\ S(R(1\left)\right)=S\left(3\right)=2 \\ S(R(2\left)\right)=S\left(2\right)=1,3 \\ S(R(3\left)\right)=S\left(2\right)=1,3 \\ \Rightarrow SoR=\left\{(3,2),(2,1),(2,3)\right\} \end{gathered}$$

Hence, the correct option is (D).