Learn what the domain, range and co-domain of a relation are, then practice finding them.
Here, R be a relation from set A to B.
The set of the first elements of all ordered pairs in R is called the domain of R.
Thus, domain of R = {x ∈ A : (x, y) ∈ R}
For example: If A = {1, 2, 3}, B = {2, 3, 4} and R = {(x, y) : y = 2x} = {(1, 2), (2, 4)}, then domain of R = {1, 2}.
Similarly, the set of the second elements of all ordered pairs in R is called the range of R.
Thus, range of R = {y ∈ B : (x, y) ∈ R}
Hence, range of R = {2, 4}.
Co-domain of Relation
Suppose R be a relation from set A to B. The set B is called the co-domain of the relation R. The range of R is always a subset of its co-domain. For example, if R is a relation from A = {1, 2, 3} to B = {2, 3, 4}, then the co-domain of R = set B = {2, 3, 4}.