Question

Let $A=\left\{1,2,3\right\}$ $B=\left\{1,3,5\right\}$. If relational $R$ from $A$ to $B$ is given by $R=\left\{\left(1,3\right),\left(2,5\right),(3,3)\right\}$. Then $R^{-1}$ is

• A. $\left\{\left(3,3\right),\left(3,1\right),(5,2)\right\}$
• B. $\left\{\left(1,3\right),\left(2,5\right),(3,3)\right\}$
• C. $\left\{\left(1,3\right),(5,2)\right\}$
• D. None of these

Answer 1

The correct option is A

$\left\{\left(3,3\right),\left(3,1\right),(5,2)\right\}$

Determine $R^{-1}$

$A=\left\{1,2,3\right\}$ [Given]

$B=\left\{1,3,5\right\}$ [Given]

$R=\left\{\left(1,3\right),\left(2,5\right),(3,3)\right\}$ [Given]

If $R$ is a relation from $A$ to $B$, then the relation $R^{-1}$ defined from $B$to $A$ by $R^{-1}=\left\{\left(b,a\right):(a,b)\in \mathrm{ℝ}\right\}$ is called the inverse of the relation $R$.

Therefore, $R^{-1}=\left\{\left(3,1\right),\left(5,2\right),(3,3)\right\}$

Hence, option (A) is the correct answer.