If the set A represents the range set for the relation R such that R = {(x, y) : x, y ∈ B and y = x - 3} is a relation on B = {0, 1, 2, 3, 4, 5} then find the set A ?

Concept:

Range of a Relation:

Let R be a relation from set A to set B. Then, the set of all second components of the ordered pair belonging to relation R forms the range of the relation R

i.e Range (R) = {b : (a, b) ∈ R}.

Calculation:

Given: Set A represents the range set for the relation R such that R = {(x, y) : x, y ∈ B and y = x - 3} is a relation on B = {0, 1, 2, 3, 4, 5}

Here, we have to find set A.

If x = 0 ⇒ y = - 3 can t be taken as it is not in B

If x = 1 ⇒ y = - 2 can t be taken as it is not in B

If x = 2 ⇒ y = - 1 can t be taken as it is not in B

If x = 3 ⇒ y = 0 can be taken as it is in B

If x = 4 ⇒ y = 1 can be taken as it is in B

If x = 5 ⇒ y = 2 can be taken as it is in B

So, the relation R can be re-written as: R = {(3, 0), (4, 1), (5, 2)}

As we know that, Range (R) = {b : (a, b) ∈ R}.

⇒ A = {0, 1, 2}

Hence, the correct option is 1.