Question

If the relation $R:A\to B$, where $A=\{1,2,3,4\}$ and $B=\{1,3,5\}$, is defined as $R=\left\{\right(x,y):x<y\text{for}x\in A,y\in B\}$, then which of the following is CORRECT?

• A. $(2,3)\in R^{-1}$
• B. Domain of $R^{-1}$ is $\{1,3,5\}$
• C. Range of $R^{-1}$ is $\{2,3,4\}$
• D. Domain of $R^{-1}$ is $\{3,5\}$

Answer 1

The correct option is D Domain of $R^{-1}$ is $\{3,5\}$

$A=\{1,2,3,4\}$ and $B=\{1,3,5\}$
$R=\left\{\right(x,y):x<y\text{for}x\in A,y\in B\}\Rightarrow R=\left\{\right(1,3),(1,5),(2,3),(2,5),(3,5),(4,5\left)\right\}\Rightarrow R^{-1}=\left\{\right(3,1),(5,1),(3,2),(5,2),(5,3),(5,4\left)\right\}$

So, $(2,3)\notin R^{-1}$
Domain of $R^{-1}$ is $\{3,5\}$
Range of $R^{-1}$ is $\{1,2,3,4\}$