Question

Let A = {1, 2, 3, ... ,14}. Define a relation R from A to A by R = {(x, y): 3x - y = 0, where x, y ∈ A}. Write down its domain, codomain and range.

Answer 1

The relation R from A to A is given as
R = {(x, y): 3x - y = 0, where x, y ∈ A}
i.e., R = {(x, y): 3x = y, where x, y ∈ A}
∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)}
The domain of R is the set of all first elements of the ordered pairs in the relation.
∴ Domain of R = {1, 2, 3, 4}
The whole set A is the codomain of the relation R.
∴ Codomain of R = A = {1, 2, 3, ..., 14}
The range of R is the set of all second elements of the ordered pairs in the relation.
∴ Range of R = {3, 6, 9, 12}