Question

What is the Domain and Range of the relation {(x,y) : x = 3y , where x and y are natural numbers less than 10} ?

• A. Domain = {0,3,6,9}
  Range = {0,1,2,3,4,5,6,7,8,9}
• B. Domain = {3,5,7,9}
  Range = {1,2,3}
• C. Domain = {3,6,9}
  Range = {1,2,3,4,5,6,7,8,9}
• D. Domain = {3,6,9}
  Range = {1,2,3}

Answer 1

The correct option is D Domain = {3,6,9}

Range = {1,2,3}
Let y = {1,2,3,4,5,6,7,8,9}
Given, x = 3y
$\therefore$ when y = 1, x = 3
when y = 2, x = 6
when y = 3, x = 9
and when y > 3, x> 10 but given that x$\ngtr$ 10.
$\therefore$ x = {3,6,9} and y = {1,2,3}.

Domain is the first set of values of the relation i.e. The Values of x. So, Domain = {3,6,9}
Range is the second set of values of the relation i.e. The Values of y. So, Range = {1,2,3}