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a) Let Fn denote the nth Fibonacci number. Show by induction that every natural number is expressible as a sum Fn1 +Fn2 +···+Fnk where ni −ni+1 > 1 for each i ≥ 1. b) Find the number of ways of tying up 7 different books into 4 bundles if the order of the books in the bundles does not matter. c) Give examples of trivially true and vacuously true statements.
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