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If A = {1, 2, 3, 4, 5, 6} and R is a relation on A such that R = {(x, y) : y = x + 1, where x and y ∈ R} then find the domain of R ?
1. {1, 3, 4, 5, 6}
2. {1, 2, 3, 4, 5}
3. {2, 3, 4, 5, 6}
4. None of these

1 Answer

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Best answer
Correct Answer - Option 2 : {1, 2, 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}.

Calculation:

Given: A = {1, 2, 3, 4, 5, 6} and R is a relation on A such that R = {(x, y) : y = x + 1, where x and y ∈ R}

when x = 1 then y = x + 1 = 2 ∈ A ⇒ (1, 2) ∈ R

when x = 2 then y = x + 1 = 3 ∈ A ⇒ (2, 3) ∈ R

when x = 3 then y = x + 1 = 4 ∈ A ⇒ (3, 4) ∈ R

when x = 4 then y = x + 1 = 5 ∈ A ⇒ (4, 5) ∈ R

when x = 5 then y = x + 1 = 6 ∈ A ⇒ (5, 6) ∈ R

when x = 6 then y = x + 1 = 7 ∉ A ⇒ (6, 7) ∉ R

So, R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

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

⇒ Domain (R) = {1, 2, 3, 4, 5}

Hence, option 2 is the correct answer.

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