Define the term of Domain, codomain and range of a relation:
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Let R be a relation from set A to set B. Then, the set of first element of the ordered pairs in R is called the domain and the set of second elements of the ordered pairs in R is called the range. The second set B is called the codomain of R.
Thus for a relation R = {(a, b); a, b ∈ R },
Domain = {a : (a, b) ∈ R} and Range = {b : (a, b) ∈ R}
For example,
If A = {16, 25, 36, 49} and B = {1, 4, 5, 6} and R be the relation “is square of ” from A to B, then
R = {(a, b) : a = b2, a ∈ A, b ∈ B}
∴ R = {(16, 4), (25, 5), (36, 6)}. Then,
Domain of R = {16, 25, 36}, Range of R = {4, 5, 6} and Codomain of R = {1, 4, 5, 6}.