Question

Let $A=\{1,2,3\},B=\{1,3,5\}$.
A relation $R:A\to B$ is defined by $R=\left\{\right(1,3),(1,5),(2,1\left)\right\}.$
Then $R^{-1}$ is defined by

• A. $\left\{\right(1,2),(3,1),(2,1\left)\right\}$
• B. $\left\{\right(1,2),(3,1),(1,3),(1,5\left)\right\}$
• C. $\left\{\right(1,2),(5,1),(3,1\left)\right\}$
• D. $R^{-1}$ is not defined

Answer 1

The correct option is C $\left\{\right(1,2),(5,1),(3,1\left)\right\}$

Using $(x,y)\in R\iff (y,x)\in R^{-1},$

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