Subspace of r containing n, Mathematics

Give an example of each of the following given below . You do not require to give any justi cation.

(a) A nonempty, bounded subset of Q with no in mum in Q.

(b) A subspace of R containing N in which {1} is open but (2) is not.

(c) A nonempty subspace of Q which is complete in the metric space sense.

(d) An uncountable open subset of R\Q which is not all of R\Q.

(e) A bounded sequence in {x € R\Q }  - 1 < x < 1} which is not Cauchy in R.

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