A relation R is defined over the set of non-negative integers as xRy ⇒ x 2+ y 2=36 what is R ?

Question

A relation R is defined over the set of non-negative integers as xRy ⇒ x 2+ y 2=36 what is R ? (A)  (0,6)  (B)  (6,0)(√11, 5),(3,3, √3) (C)  (6,0)(0,6)  (D) (√11, 5),(2,4 √2),(5 √11),(4 √2,2)

Tardigrade Admin · Accepted Answer

R is defined over the set of non negative integers, x2+y2=36 ⇒ y=√36-x2 =√(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)

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

${(0, 6)}$

${(6, 0) (11, 5), (3, 3, 3)$

${(6, 0) (0, 6)}$

$(11, 5), (2, 42), (5 11), (4 2, 2)}$

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

Q. A relation R is defined over the set of non-negative integers as xRy⇒x2+y2=36 what is R ?

{(0,6)}

{(6,0)(11​,5),(3,3,3​)

{(6,0)(0,6)}

(11​,5),(2,42​),(511)​,(42,2​)}