Question

Let R be the relation on the set N of natural numbers defined by R={(a,b):a+3b=12,a,b belongs to natural number find R,domain of R and range of R

Answer 1

Answer:

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

Domain of R = { 9 , 6 , 3 }

Range of R = { 1 , 2 , 3 }

Step-by-step explanation:

Since we are given that

R = { (a,b):a+3b=12 ∧ a,b ∈ N }.

The condition is following

a + 3b=12              a,b belongs to natural number

If b = 1 we get a = 9

So (9 , 1) ∈ R

If b = 2 then a = 6

So

(6 , 2) ∈ R

If b = 3 then a = 3

so

(3 , 3) ∈ R  

And

if b ≥ 4  then

a = 0 or a < 0 so a ∉ B for b ≥ 4

And so (a , b) ∉ R for b ≥ 4

Thus

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

And

Domain of R = first elements of all order pairs = { 9 , 6 , 3 }

Thus

Domain of R = { 9 , 6 , 3 }

And

Range of R = Set of final elements of order = { 1 , 2 , 3 }

Thus

Range of R = { 1 , 2 , 3 }

Answer 2

Answer:

Step-by-step explanation: