Question

The relation $R$ defined on the set $A=[1,2,3,4,5]$ by $R=\left[(x,y):\left|x^2-y^2\right|<16\right]$ is given by,

• A. $[(1,1),(2,1)(3,1),(4,1),(2,3)]$
• B. $[(2,2),(3,2)(4,2),(2,4)]$
• C. $[(3,3),(3,4)(5,4),(4,3),(3,1)]$
• D. None of these

Answer 1

Answer: (D)

Here, $R=\left\{(x,y):\left|x^2-y^2\right|<16\right\}$ and $A=\{1,2,3,4,5\}$
$\therefore R=[(1,2),(1,3),(1,4);(2,1),(2,2),(2,3),(2,4);(3,1),$
$(3,2)(3,3),(3,4);(4,1),(4,2),(4,3);(4,4),(4,5);(5,4),(5,5)]$