If R= (x, y): x, y ∈ Z, x2+3 y2 ≤ 8 is a relation on the set of integers Z, then the domain of R -1 is :

Question

If R= (x, y): x, y ∈ Z, x2+3 y2 ≤ 8 is a relation on the set of integers Z, then the domain of R -1 is : (A)  -2,-1,1,2  (B)  -1,0,1  (C)  -2,-1,0,1,2  (D)  0,1

Tardigrade Admin · Accepted Answer

R = ( x , y ): x , y ∈ z , x 2+3 y 2 ≤ 8 For domain of R -1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/66f888a20bdd564c5ec503d387125d0e-.png" /> Collection of all integral of y's For x=0, 3 y2 ≤ 8 ⇒ y ∈ -1,0,1

Q. If $R = {(x, y) : x, y \in Z, x^{2} + 3 y^{2} \leq 8}$ is a relation on the set of integers $Z$ , then the domain of $R^{- 1}$ is :

${- 2, - 1, 1, 2}$

${- 1, 0, 1}$

${- 2, - 1, 0, 1, 2}$

${0, 1}$

$R = {(x, y) : x, y \in z, x^{2} + 3 y^{2} \leq 8}$
For domain of $R^{- 1}$

Collection of all integral of y's
For $x = 0, 3 y^{2} \leq 8$
$\Rightarrow y \in {- 1, 0, 1}$

Q. If R={(x,y):x,y∈Z,x2+3y2≤8} is a relation on the set of integers Z, then the domain of R−1 is :

{−2,−1,1,2}

{−1,0,1}

{−2,−1,0,1,2}

{0,1}