Prove using weak or strong induction as needed. State which one you use (a) Prove that every positive integer n has a binary expansion. Namely, that there exists integers c; € {0, 1} such that n=0C₂2² (b) Let {a;} be a sequence of sequence of real numbers such that Vij ai+j ≤ai + aj Prove that o i/i> an (c) Prove by strong induction that if a country has n cities where any two cities are connected by a one-way road, there is a route that passes through every city.

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