Question

If set A = {2, 3,4,7} and set B ={3, 4,5,6} write the relation In roaster form in arrow diagram and also write domain and range

Answer 1

Answer:

For the required Relation we have to find the ordered pairs where x co-ordinate is from set A which is mapped to the y co-ordinate from set B.

So, the relation is {(5,a),(5,b),(7,b),(7,c),(9,a),(9,b),(9,c)}

Domain is the set of all x co-ordinates ={5,7,9}

Range is the set of all y co-ordinates ={a,b,c}.

Answer 2

Step-by-step explanation:

In domain and range of a relation, if R be a relation from set A to set B, then

• The set of all first components of the ordered pairs belonging to R is called the domain of R.

Thus, Dom(R) = {a ∈ A: (a, b) ∈ R for some b ∈ B}.

• The set of all second components of the ordered pairs belonging to R is called the range of R.

Thus, range of R = {b ∈ B: (a, b) ∈R for some a ∈ A}.

Therefore, Domain (R) = {a : (a, b) ∈ R} and Range (R) = {b : (a, b) ∈ R}

Note:

The domain of a relation from A to B is a subset of A.

The range of a relation from A to B is a subset of B.

For Example:

If A = {2, 4, 6, 8) B = {5, 7, 1, 9}.

Let R be the relation ‘is less than’ from A to B. Find Domain (R) and Range (R).

Solution:

Under this relation (R), we have

R = {(4, 5); (4, 7); (4, 9); (6, 7); (6, 9), (8, 9) (2, 5) (2, 7) (2, 9)}

Therefore, Domain (R) = {2, 4, 6, 8} and Range (R) = {1, 5, 7, 9}