Question

A relation $R$ is defined over the set of non-negative integers as $xRy\Rightarrow x^2+y^2=36$. What is $R$?

• A. $\left\{(0,6)\right\}$
• B. $\left\{(6,0)(\surd 11,5),(3,3\surd 3)\right\}$
• C. $\left\{(6,0),(0,6)\right\}$
• D. $\left\{(\surd 11,5),(2,4\surd 2),(5,\surd 11),(4\surd 2,2)\right\}$

Answer 1

The correct option is C

$\left\{(6,0),(0,6)\right\}$

Explanation for the correct option:

Given, $x^2+y^2=36$

R is defined over the set of non negative integers

$y=\surd 36-x^2=\surd (6-x)(6+x)$

$\Rightarrow x=0or6$

for $x=0,y=6$

and for $x=6,y=0$

So, $R=\left\{(6,0),(0,6)\right\}$

Hence, Option ‘C’ is Correct.