Find the interior, boundary and closure of the following sets A in  with the usual metric and discrete metric.

i) A =  , the set of rationals in 

ii) 

i) \( A = \mathbb{Q} \), the set of rationals in \( \mathbb{R} \):

In the usual metric space:
- Interior: The interior of \( \mathbb{Q} \) in \( \mathbb{R} \) is empty because every real number has an open neighborhood containing irrational numbers.
- Boundary: The boundary of \( \mathbb{Q} \) in \( \mathbb{R} \) is \( \mathbb{R} \) because every real number is a limit point of both rational and irrational numbers.
- Closure: The closure of \( \mathbb{Q} \) in \( \mathbb{R} \) is \( \mathbb{R} \) because it includes _________ ___ ____ __________ ____ _______.
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