Question

The relation $R$ is defined on the set of natural numbers as $\left\{\right(a,b):a=2b\}.$
Then $R^{-1}$ is given by

• A. None of these
• B. $R^{-1}$ is not defined
• C. $\left\{\right(2,1),(4,2),(6,3)\dots ..\}$
• D. $\left\{\right(1,2),(2,4),(3,6)\dots .\}$

Answer 1

The correct option is D $\left\{\right(1,2),(2,4),(3,6)\dots .\}$

Using $(x,y)\in R\iff (y,x)\in R^{-1},$
Here $R=\left\{\right(a,b):a=2b\}\text{where}a,b\in N$
$\Rightarrow R=\left\{\right(2,1),(4,2),(6,3),\dots \dots \}$
So, $R^{-1}=\left\{\right(1,2),(2,4),(3,6),\dots \dots \}$.