Question

If R = $\left\{\left(x,y\right):x^2+y^2\le 4,x,y\in Z\right\}$ is a relation in Z, then the domain of R is ______________________.

Answer 1

Given: R = $\left\{\left(x,y\right):x^2+y^2\le 4,x,y\in Z\right\}$

R = {(−2, 0), (2, 0), (0, 2), (0, −2), (−1, 1), (−1, −1), (1, −1), (1, 1), (0, 1), (1, 0), (−1, 0), (0, −1), (0, 0)}

Therefore, Domain of R = {−2, −1, 0, 1, 2}

Hence, if R = $\left\{\left(x,y\right):x^2+y^2\le 4,x,y\in Z\right\}$ is a relation in Z, then the domain of R is {−2, −1, 0, 1, 2}.