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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.
Let R be the relation on S = {1, 2, 3, 4, 5} defined by R = {(1,3); (1, 1); (3, 1); (1, 2); (3, 3); (4, 4)}. (b) Write down the matrix of R. (c) Draw the digraph of R.
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