Write the domain of the relation R defined on the set Z of integers as follows:
(a, b) ϵR ⬄ a2 + b2 = 25
Given a and b are integers, i.e. a,b ∈ Z.
∴ Domain of R = Set of all first elements in the relation.
= Values of ‘a’ which are in the relation.
=Z (Integers)
Range of R=Set of all second elements in the relation.
=Values of ‘b’ which are in the relation.
=Z(Integers)
Since, a2+ b2 = 25 and a, b are integers;
⇒ R= {(5,0), (0,5), (-5,0), (0, -5), (3,4), (4,3), (-3, -4), (-4, -3),
(-3,4), (4, -3), (-4,3), (3, -4)}
⇒ Domain of R= {-5, -4, -3,0,3,4,5}