Question

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

• A. $\left\{\right(1,2),(3,1),(1,3),(1,5\left)\right\}$
• B. $\left\{\right(1,2),(3,1),(2,1\left)\right\}$
• C. $\left\{\right(1,2),(5,1),(3,1\left)\right\}$
• D. $\left\{\right(1,3),(1,5),(2,1\left)\right\}.$

Answer 1

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

We know that
$(x,y)\in R⟺(y,x)\in R^{-1}$

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