Question

find the domain and range of the relation r={(x,y) :x+y=8 and x, y are natural numbers} ​

Answer 1

Step-by-step explanation:

Let x = { 1 , 2 , 3 }

than,

if x = 1 , y = 7

x = 2 , y = 6

x = 3 , y = 5

hence,

domain = 123

range = 567

Answer 2

• Domain of the relation = {1 , 2 , 3 , 4 , 5 , 6 , 7}

• Range of the relation = {1 , 2 , 3 , 4 , 5 , 6 , 7}

Given :

The relation R = {(x,y) : x + y = 8 and x , y are natural numbers}

To find :

The domain and range of the relation

Solution :

Step 1 of 3 :

Find the relation R

Here the given relation is

R = {(x,y) : x + y = 8 and x , y are natural numbers}

For x = 1 , y = 7

∴ (1,7) ∈ R

For x = 2 , y = 6

∴ (2,6) ∈ R

For x = 3 , y = 5

∴ (3,5) ∈ R

For x = 4 , y = 4

∴ (4,4) ∈ R

For x = 5 , y = 3

∴ (5,3) ∈ R

For x = 6 , y = 2

∴ (6,2) ∈ R

For x = 7 , y = 1

∴ (7,1) ∈ R

Thus the relation is given by

R = { (1,7) , (2,6) , (3,5) , (4,4) , (5,3) , (6,2) , (7,1) }

Step 2 of 3 :

Find domain of the relation

Domain of the relation

= {x : (x,y) ∈ R }

= {1 , 2 , 3 , 4 , 5 , 6 , 7}

Step 3 of 3 :

Find range of the relation

Range of the relation

= {y : (x,y) ∈ R }

= {7 , 6 , 5 , 4 , 3 , 2 , 1}

= {1 , 2 , 3 , 4 , 5 , 6 , 7}

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ consider the above set A. Insert the appropriate symbol E of E/ in each of the following blank spaces (a) -3...A (b) 9.....

https://brainly.in/question/28046206

2. if A ={2,3} and B= { x|x is solution of x^2 + 5x + 6= 0}

Are there A and B equal set or disjoint set?

https://brainly.in/question/21681247

#SPJ2