Question

Assume that A = {1, 2, 3,…,20}. Define a relation R from A to A by R = {(x, y) : 3x – y = 0, such that x, y ∈ A}. Determine R in Roster form and write down its range, domain, and co-domain.

Answer 1

Answer:

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

Answer 2

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It is given that the relation R from A to A is given by R = {(x, y): 3x – y = 0, where x, y ∈ A}.

It means that R = {(x, y) : 3x = y, where x, y ∈ A}

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

We know that the domain of R is defined as the set of all first elements of the ordered pairs in the given relation.

Hence, the domain of R = {1, 2, 3, 4}

To determine the codomain, we know that the entire set A is the codomain of the relation R.

Therefore, the codomain of R = A = {1, 2, 3,…,14}

As it is known that, the range of R is defined as the set of all second elements in the relation ordered pair.

Hence, the Range of R is given by = {3, 6, 9, 12}

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