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.

Given: A = {1, 2, 3, ..., 14} and R = {(x, y) : 3x – y = 0, where x, y ∈ A}

As the relation R from A to A is given as:

R = {(x, y) : 3x – y = 0, where x, y A}

⇒ R = {(x, y) : 3x = y, where x, y A}

Hence the relation in roaster form, R = {(1, 3), (2, 6), (3, 9), (4, 12)}

As Domain of R = set of all first elements of the order pairs in the relation.

⇒ Domain of R = {1, 2, 3, 4}

Codomain of R = the whole set A

⇒ Codomain of R = {1, 2, 3, ..., 14}

Range of R = set of all second elements of the order pairs in the relation.

⇒ range of R = {3, 6, 9, 12}.