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Question
If R3 = {(x, x) | x is a real number} is a relation. Then find domain and range of R3.
Solution
R3 = {(x, x) | x is a real number} is a relation
Domain of R3 consists of all the first elements of all the ordered pairs of R3,
i.e., x,
It is also given that x is a real number,
So, Domain of R3 = R
Range of R contains all the second elements of all the ordered pairs of R3,
i.e., |x|
It is also given that x is a real number,
So, |x| = |R|
⇒ |x| ≥ 0
i.e., |x| has all positive real numbers including 0
Hence,
Range of R3 = `[0, oo)`
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