If A = {x ∈ N : 1 ≤  x ≤ 10} and let R be a relation defined on A such that R = {(x, y) : y = 2x - 1, x, y ∈ A} then find the domain of R?

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 = {x ∈ N: 1 ≤  x ≤ 10} and R is a relation defined on A such that R = {(x, y) : y = 2x - 1, x, y ∈A}

⇒ A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

As, R = {(x, y) : y = 2x - 1 where x, y ∈A}

⇒ R = {(1, 1), (2, 3), (3, 5), (4, 7), (5, 9)}

As we know that, the set of all first components of the ordered pair belonging to relation R forms the domain of the relation R.