Question

Let A = {1, 2, 3, 4) and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12). 2 Let R = {(1,3), (2,6), (3,10), (4,9)} = AxB be a relation. Show that R is a function and find its domain, co-domain and the range of R.​

Answer 1

Given :-

• A = { 1 , 2 , 3 , 4 }

• B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

• R = {(1,3), (2,6), (3,10), (4,9)}

To prove :-

• R is a function

• Domain, co-domain , range = ?

Solution :-

Since each and every element of set A in the given relation has only one image in set B, so it's clear that R is a function.

The whole set A in the ordered pair is called domain whereas whole set B in this ordered pair is called co-domain.

So,

DOMAIN = { 1 , 2 , 3 , 4 }

CO-DOMAIN = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

The set of all second elements of the relation R are called range.

so,

RANGE = { 3 , 6 , 10 , 9 }

More :-

• Every function is a relation but all relations can't be termed as functions.

• A function f from set A to B is a special type of relation for which every element of set A has one and only one image in set B.

We can write f : A → B , where f(x) = y.