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 ∈ A}. Determine and write down its range, domain, and codomain.​

Answer 1

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$\Large\fbox{\color{purple}{QUESTION}}$

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 ∈ A}. Determine and write down its range, domain, and codomain.

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️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}

$\Large\mathcal\green{FOLLOW \: ME}$

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Answer 2

Answer:

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

Domain of R=set of all first elaments of the orderd pairs={1,2,3,4}

Range of R=set of all second elements of the ordered pairs={3,6,9,12

Codomain R is defined from A to A

Codomain of R = A{1,2,3,...,14}

Step-by-step explanation:

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