Question

If A and B are the domain and range respectively for the relation R such that R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}} then which of the following option is true ?
1. A = {0, 1, 2, 3, 4, 5} and B = {5, 6, 7, 8, 9, 10}
2. A = {1, 2, 3, 4, 5} and ​B = {6, 7, 8, 9, 10}
3. A = {0, 1, 2, 3, 4} and ​B = {5, 6, 7, 8, 9}
4. None of these

Answer 1

Correct Answer - Option 1 : A = {0, 1, 2, 3, 4, 5} and B = {5, 6, 7, 8, 9, 10}

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 = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}

So, the relation R can be re-written as: R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}

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

⇒ A = {0, 1, 2, 3, 4, 5}

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

⇒ B = {5, 6, 7, 8, 9, 10}

Hence, option 1 is the correct answer.