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. $\{(0,6)\}$
• B. $\{(6,0)(\sqrt{11}, 5),(3,3, \sqrt{3})$
• C. $\{(6,0)(0,6)\}$
• D. $(\sqrt{11}, 5),(2,4 \sqrt{2}),(5 \sqrt{11)},(4 \sqrt{2,2})\}$

Answer 1

Answer: (C)

$R$ is defined over the set of non negative integers,
$x^{2}+y^{2}=36$
$ \Rightarrow y=\sqrt{36-x^{2}}$
$=\sqrt{(6-x)(6+x)}, x=0$
or 6 for $x=0, y=6$ and for
$x=6, y=0$ So, $y$ is $6$ or $0$
so, $R =\{(6,0),(0,6)\}$