Math, asked by sejalg894, 8 months ago

30. 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.​

Answers

Answered by Anonymous
533

\huge \bold{ \underline { \bf \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.

\huge \bold{ \underline { \bf \orange{Answer↴ }}}

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

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

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

 \large\sf { \implies 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  \large\bold{\sf {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  \large\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.

 \large\bold{\rm\red {Hence, \: the \:  Range \:  of \: R \: is \: given \: by \: = {3, 6, 9, 12}}}

Answered by Anonymous
12

\huge \bold{ \underline { \bf \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.

\huge \bold{ \underline { \bf \orange{Answer↴ }}}

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

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

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

 \large\sf { \implies 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  \large\bold{\sf {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  \large\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.

 \large\bold{\rm\red {Hence, \: the \:  Range \:  of \: R \: is \: given \: by \: = {3, 6, 9, 12}}}

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