Question

Q)Let A= {1,2,3,4...20}.
Define a relation 'R' from A to A by R={(x,y):3x-y30,where x,y belongs to A}.Write R in rooster form and hence find its domain, range and codomain.​

Answer 1

Step-by-step explanation:

A={1,2,3...20}

3x-y=0 , 3x=y

X=1;y=3×1=3

X=2;y=3×2=6

X=3;y=3×3=9

X=4;y= 3×4=12

X=5;y=3×5=15

x=6;y=3×6=18. (as 7×3 is 21 and is greater than 20

we didn't take 7as X)

R={(1,3),(2,6),(3,9),(4,12),(5,15),(6,18)}

domain={1,2,3,4,...20}

codomain={1,2,3,....20}

range ={3,6,9,12,15,18}

Answer 2

${\huge {\boxed{\bold{\boxed{\mathfrak{\color{Blue}{Answer}}}}}}}$

It is given that the relation R from A to A is given by R = {(x, y): 3x – y = 0, where x, y ∈ A}.

It means that R = {(x, y) : 3x = y, where x, y ∈ A}

Hence, R = {(1, 3), (2, 6), (3, 9), (4, 12)}

We know that the domain of R is defined as the set of all first elements of the ordered pairs in the given relation.

Hence, the domain of R = {1, 2, 3, 4}

To determine the codomain, we know that the entire set A is the codomain of the relation R.

Therefore, the codomain of R = A = {1, 2, 3,…,14}

As it is known that, the range of R is defined as the set of all second elements in the relation ordered pair.

Hence, the Range of R is given by = {3, 6, 9, 12}

Hope it's Helpful.....:)