Question

The relation $R$ defined on the set $A=\{1,2,3,4\}$ by $R=\left\{\right(x,y):|x^2-y^2|<10,x,y\in A\}$ is given by

• A. $\left\{\right(1,1),(1,2),(1,3),(2,2),(2,3),(3,3),(3,4),(4,4\left)\right\}$
• B. $\left\{\right(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4\left)\right\}$
• C. $\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,3),(3,4),(4,3),(4,4\left)\right\}$
• D. None of these

Answer 1

The correct option is C $\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,3),(3,4),(4,3),(4,4\left)\right\}$

If $x=1$, then $y$ can be $1,2,3$.
If $x=2$, then $y$ can be $1,2,3$.
If $x=3$, then $y$ can be $1,2,3,4$.
If $x=4$, then $y$ can be $3,4$.
$\therefore R=\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3),(3,4),(4,3),(4,4\left)\right\}$
$\therefore$ The correct answer is $C$.