Question

Let N be the set of natural numbers and the relation R be defined on N such that
R={(x,y);y=2x,x,y $ϵ$ N}.
What is the domain, codomain, and range of R?
Is this relation a function?

Answer 1

R={(x,y);Y=2x, x,y $ϵ$ N}
Step 1: Convert relation R in roster from
Put x =1,2,3,... in y =2x, we get y=2,4,6,...
So, relation R is {(1,2), (2,4), (3,6),....}
Step 2: Domain of relation R
Domain =,Set of first elements of ordered pairs of relation R
={1,2,3,4,...}
=N
Step 3: Co-domain of relation R
$\because yϵN$
$\therefore$ Co-domain of R is {1,2,3,.-}=N
Given R={(x,y):y=2x, x,y $ϵ$ N}
Step 4: Range of relation R
Range=Set of second elements of ordered pirs of relation R
={2,4,6,8,...}
Step 5: Checking whether R is a function or not
Since, every element has one and only one image, therefore this relation is a function
$\therefore$ The domain and co-domain of R is the set of natural numbers N and range is the set of even natural numbers.
Relation R is a fuction