Question

The relation R = {(x, y) : x, y ∈ Z, x² + y² = 64} is __________.

Answer 1

R = {(x, y) : x, y ∈ Z : x² + y² = 64}
Since
x² + y² = 64
y² = 64 − x²
The only possibilities for x are 0, 8 and −8, and for y are 0, −8 and 8 .
i.e R = {(0, 8), (8, 0), (−8, 0) (0, −8)}
Hence R = { (0, 8) (−8, 0) (8, 0) (0, −8)}