Q. 93.5( 2 Votes )

# 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?

Answer :

x^{2} + y^{2} = 9

We can have only integral values of x and y.

Put x = 0 , y = 3 , 0^{2} + 3^{2} = 9

Put x = 3 , y = 0 , 3^{2} + 0^{2} = 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}

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