Question

Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.​

Answer 1

Given :

• A = {1 , 2 , 3...14}

To Find :

• Domain , Co-domain and Range .

Solution :

$\longmapsto\tt{3x-y=0}$

$\longmapsto\tt{{\not{-}}y={\not{-}}3x}$

$\longmapsto\tt\bf{y=3x}$

Putting x = 1 :

$\longmapsto\tt{y=3(1)}$

$\longmapsto\tt\bf{y=3}$

Putting x = 2 :

$\longmapsto\tt{y=3(2)}$

$\longmapsto\tt\bf{y=6}$

Putting x = 3 :

$\longmapsto\tt{y=3(3)}$

$\longmapsto\tt\bf{y=9}$

Putting x = 4 :

$\longmapsto\tt{y=3(4)}$

$\longmapsto\tt\bf{y=12}$

Now ,

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

Domain = {1 , 2 , 3 , 4}

Codomain = {1 , 2 , 3 ... 14}

Range = {3 , 6 , 9 , 12}

____________________

Domain :

Set of all first elements is known as Domain .

Range :

Set of all second elements is known as Range .

____________________

Answer 2

Step-by-step explanation:

Now, given that

3x-y=0

y=3x

Putting x=1

y=3×1=3

Putting x =2

y=6

Putting x=3

y=9

Putting x=4

y=12

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

Domain of R = {1,2,3,4}

Range of R={3,6,9,12}

Codomain

R referred from A to A

So, Codomain Of R=A

={1,2,3,4...12}