Let R be a relation on Z, defined by (x, y) ϵ R ↔ x 2 + y 2 = 9. Then, write R as a set of ordered pairs. What is its domain?

Question

Philoid · Accepted Answer

x² + y² = 9

We can have only integral values of x and y.

Put x = 0 , y = 3 , 0² + 3² = 9

Put x = 3 , y = 0 , 3² + 0² = 9

R = {(0, 3) , (3, 0) , (0 , -3) , (-3 , 0)}

The domain of R is the set of first co-ordinates of R

Dom(R) = {-3 , 0 , 3}

The range of R is the set of second co-ordinates of R

Range(R) = {-3 , 0 , 3}