Question

Find the range of the following relations
R = {(a,b): a, b e N and 2a + b = 10).​

Answer 1

Answer:

Let R={(a,b):a,b∈N and 2a+b=10}. Show that R is a binary relation on N

Step-by-step explanation:Here `R={(a,b):a,b inN" and "2a+b=10}.`

Now, `2a+b=10impliesb=(10-2a).`

`:." "(a=1impliesb=8),(a=2impliesb=6),(a=4impliesb=2).`

`:." "R={(1,8),(2,6),(3,4),(4,2)}.`

Since `RsubNxxN`, so R is a binary relation on N.

Dom (R)=set of 1st coordinates of elements of R

`={1,2,3,4}.`

Range (R)=set of 2nd coordinates of elements of R

`={8,6,4,2}.`

Co-domain of R=N.