Question

If A and B are the domain and range respectively for the relation R such that R = {(x, x³ - 1) : x ∈ {1, 3, 5, 7, 9}} then which of the following option is true ?
1. A = {0, 26, 124, 342, 728} and B = {1, 3, 5, 7, 9}
2. A = {0, 26, 63, 342, 511} and B = {1, 3, 5, 7, 9}
3. A = {1, 3, 5, 7, 9} and B = {0, 26, 124, 342, 728}
4. A = {1, 3, 5, 7, 9} and B = {0, 7, 124, 215, 728}

Answer 1

Correct Answer - Option 3 : A = {1, 3, 5, 7, 9} and B = {0, 26, 124, 342, 728}

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, x3 - 1) : x ∈ {1, 3, 5, 7, 9}}

So, the relation R can be re-written as: R = {(1, 0), (3, 26), (5, 124), (7, 342), (9, 728)}

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

⇒ A = {1, 3, 5, 7, 9}

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

⇒ B = {0, 26, 124, 342, 728}