Question

If A and B are the domain and range respectively for the relation R such that R = {(5, 3), (6, 4), (7, 5)} then which of the following option is true ?
1. A = {3, 6, 7} and ​B = {3, 4, 5}
2. A = {5, 6, 7} and ​B = {3, 4, 6}
3. A = {5, 6, 7} and B = {3, 4, 5}
4. None of these

Answer 1

Correct Answer - Option 3 : A = {5, 6, 7} and B = {3, 4, 5}

Concept:

Domain of a Relation: Let R be a relation from set A to set B. Then, the set of all first components of the ordered pair belonging to relation R forms the domain of the relation R i.e Domain (R) = {a: (a, b) ∈ R}.

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: A and B are the domain and range respectively for the relation R such that R = {(5, 3), (6, 4), (7, 5)}

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

⇒ A = {5, 6, 7}

We also know that Range (R) = {b: (a, b) ∈ R}.

⇒ B = {3, 4, 5}

Hence, option 3 is the correct answer.