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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.
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Solution
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}
= {(x, 3x), where x, 3x ∈ A}
∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)}
`[∵ 1 ≤ 3x ≤ 14, ∴ 1/3 ≤ x ≤ 14/3 ⇒ x = 1, 2, 3, 4]`
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}
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