Question

Let R be a relation on Z, defined by (x, y)ϵR ↔ x² + y² = 9. Then, write R as a set of ordered pairs. What is its domain?

Answer 1

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}