Question

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.​

Answer 1

\huge \bold{ \underline { \bf \purple{Question↴}}}

Question↴

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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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Answer↴

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

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

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

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\large\sf { \implies R = {(1, 3), (2, 6), (3, 9), (4, 12)}}⟹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 \large\bold{\sf {R = {1, 2, 3, 4}}}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 \large\sf {R = A = {1, 2, 3,…,14}}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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\large\bold{\rm\red {Hence, \: the \: Range \: of \: R \: is \: given \: by \: = {3, 6, 9, 12}}}Hence,theRangeofRisgivenby=3,6,9,12

Answer 2

Answer:

The relation R from A to A is given as

R={(x,y):3x−y=0;x,y∈A}

i.e., R={(x,y):3x=y;x,y∈A}

∴R={(1,3),(2,6),(3,9),(4,12)}

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 co-domain 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}