If R = {(x,y): x2 + y2 ≤ 4; x,y ϵ Z} is a relation of Z, write the domain of R.
Given x and y are integers, i.e x,y ∈ Z.
∴ Domain of R = Set of all first elements in the relation.
= Values of ‘x’ which are in the relation.
=Z (Integers)
Range of R=Set of all second elements in the relation.
=Values of ‘y’ which are in the relation.
=Z(Integers)
Since, x2+ y2 ≤ 4 and x,y are integers;
⇒ R= {(0,0), (1,0), (0,1), (-1,0), (0,-1), (1,1), (-1,-1), (-1,1),
(1,-1), (0,2), (0,-2), (2,0), (-2,0)}
⇒ Domain of R= {-2,-1,0,1,2}