Question

Assume that A = {1, 2, 3,...,14}.

Define a relation R from A to A by R =
{(x, y): 3x - y = 0, such that x, y E A}.

Determine and write down its range,
domain, and codomain.​

Answer 1

$\huge\boxed{\fcolorbox{pink}{ink}{Answer}}$

★It is given that the relation R from A to A is given by,

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

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It means that,

$\sf {R = {(x, y) : 3x = y, where x, y ∈ A}}$

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$\sf { \implies R = {(1, 3), (2, 6), (3, 9), (4, 12)}}$

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

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

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

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

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

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${\rm\purple {Hence, \: the \: Range \: of \: R \: is \: given \: by \: = 3,6,9,12}}$

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Answer 2

★It is given that the relation R from A to A is given by,

‎

It means that,

$\sf {R = {(x, y) : 3x = y, where x, y ∈ A}}$

‎

R = {(1, 3), (2, 6), (3, 9), (4,8)}

‎

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${\sf {R = {1, 2, 3, 4}}}$

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

‎

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

‎

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