Question

Let $R$ be a relation on $N$ defined by $R=\{(1+x,1+x^2):x\le 5,x\in N\}.$ Which of the following statements is FALSE?

• A. $R=\left\{\right(2,2),(3,5),(4,10),(5,17),(6,26\left)\right\}$
• B. Domain of $R$ is $\{2,3,4,5,6\}$
• C. Range of $R$ is $\{2,5,10,17,26\}$
• D. Range of $R^{-1}$ is $\{1,2,3,4,5\}$

Answer 1

The correct option is D Range of $R^{-1}$ is $\{1,2,3,4,5\}$

Put $x=1,2,3,4,5$
Domain of $R$ is $\{2,3,4,5,6\}$
Range of $R$ is $\{2,5,10,17,26\}$
$R=\left\{\right(2,2),(3,5),(4,10),(5,17),(6,26\left)\right\}$
Range of $R^{-1}$ is $\{2,3,4,5,6\}$