Question

The relation $R$ defined in $A=\{1,2,3,\}$ by $aR$ $b$ if $|a^2-b^2|\le 5$. Which of the following is false?

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

Answer 1

The correct option is D Range of $R=\left\{5\right\}$

$R=\left\{\right(1,1),(2,2),(3,3),(2,1),(1,2),(2,3),(3,2\left)\right\}$

Clearly $R^{-1}=R$

Domain $=\{1,2,3\}$ Range $=\{1,2,3\}$

Hence option 'D' is a false statement with regard to $R$.