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

Given:

The relation R from A to A

Then,

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

= {(x, y): 3x = y, where x, y ∈ A}

So,

R = {(1, 3), (2, 6), (3, 9), (4, 12)}

Now,

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}

Therefore:

Domain of R = {1, 2, 3, 4}

Codomain of R = A = {1, 2, 3, …, 14}

Range of R = {3, 6, 9, 12}