Question

A relation defined from $A=\{0,1,2,3,4\}$ to $N$ as $xRy\text{iff}x=y$. Then which among the following options is correct

• A. $R^{-1}$ is a function with range as $A$
• B. $R$ is a function with range as $N$
• C. $R$ is a function with range as $\{1,2,3,4\}$
• D. $R$ is not a function

Answer 1

The correct option is D $R$ is not a function

Here $R=\left\{\right(1,1),(2,2),(3,3),(4,4\left)\right\}$
As $0\in A$ but doesn't have any image in $N$
So, it is not a function

Here$R^{-1}=\left\{\right(1,1),(2,2),(3,3),(4,4\left)\right\}$
As $5\in N$ but doesn't have any image in $A$
So, it is not a function