Question

$\mathfrak{\large{\underline{\underline{Question :-}}}}$

Let A = {1,2,3 ...... 14} Define a relation from A to A by R = {(x,y): 3x - y = 0 , Where x, y $\in$ A}.

Write down its domain, codomain and range.

No spams !!! ​

Answer 1

Answer:

Domain = { 1 , 2 , 3 , 4 }

Range = { 2 , 6 , 9 , 12 }

Codomain = A  i.e . { 1 , 2 , 3  ......  14 } .

Step-by-step explanation:

Given :

Set A = { 1 , 2 , 3  ......  14 }

And it is defined by relation R = { ( x , y ) : 3 x - y = 0 , Where x, y ∈  A }.

We have to find domain, co domain and range of R.

Well firstly we should know what are they :

Domain :  First element of cartesian product defined by any relation .

Range : Second element of cartesian product defined by any relation .

Co domain : Whole second of the any relation .

Coming back to question :

A = { 1 , 2 , 3  ......  14 }

R = { ( x , y ) : 3 x - y = 0 , Where x, y ∈  A }

3 x - y = 0

3 x = y

when     x = 1      then   y = 3

when     x = 2     then   y = 6

when     x = 3     then   y = 9

when     x = 4      then   y = 12

After that y value will be come 15 which is not belongs to set A .

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

Domain = { 1 , 2 , 3 , 4 }

Range = { 2 , 6 , 9 , 12 }

Codomain is rest of other element :

Codomain = A  i.e . { 1 , 2 , 3  ......  14 } .

Thus we get all answers .

Answer 2

Chapter 2

Class 11

Relations and Functions.

Answer :

• Domain = { 1 , 2 , 3 , 4 }  
• Range = { 3 , 6 , 9 , 12 }  
• Codomain = A = { 1 , 2 , 3  ......  14 }.

★ Explanation :

Given :

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

R = {(x,y): 3x - y = 0. where {x, y ∈ A}.

To Do :

We have to write down its domain, codomain and range.

Solution :

As per given condition we can say,

⇒ 3x - y = 0.

⇒ 3x = 0 + y.

⇒ 3x = y.

∴ y = 3x.

$\rule{300}{1.5}$

★ Remember -

$\begin{tabular}{|c|c|}\cline{1-2} Value of x& Value of y=3x \\\cline{1-2}\ 1 &3\times 1=3 \\\cline{1-2}\ 2 & 3\times 2=6\\\cline{1-2}\ 3 &3\times 3=9\\\cline{1-2}\ 4 &3\times4 =12\\\cline{1-2}\ 5 &3\times 5 = 15\\\cline{1-2}\ 6 & 3\times 6=18 \\\cline{1-2}\ 7& 3\times7=21 \\\cline{1-2}\end{tabular}$

Now,

Value of x   Whether x , y ∈ A

1                  →           Yes.  

2                 →           Yes.

3                 →           Yes.

4                 →            Yes.

5                 →              No.

6                 →               No.

7                 →                 No.

$\rule{300}{1.5}$

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

Now,

Domain of R :

⇒ {1 , 2 , 3 , 4}

Range of R :

⇒ { 3 , 6 , 9 , 12}

Co - Domain :

Co - Domain of R = A

⇒ { 1 , 2 , 3.....,14}

$\rule{300}{1.5}$

★ Extra Information :

Domain :

Set of all first elements of the ordered pairs in the relation.

★ Range :

Set of all second elements of the ordered pair in the relation.

★ Co - Domain :

The set that contains all the possible values of a given relation.