3. (i) Let {I1, I2, I3, · · ·} be a set of nested closed intervals, that is In+1 C In for all n. Prove that ... 8. n In # Ø i=1 (ii) Show that the above result need not hold if each In is allowed to be an open interval. (iii) Let {I1, I2, · , In} be a set of n intervals for some n > 3. Assume that they are pairwise intersecting, that is I; nI; # Ø for all i # j. Show using induction that n i=1 Does this contradict (ii) ? Justify your answer.

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