28 PS5 - Handout #28 April 26, 2010 CS103 Robert Plummer...

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Handout #28 CS103 April 26, 2010 Robert Plummer Problem Set #5—Due Monday, May 5 in class Note : no late days may be used on this assignment since our midterm is the next day! These problems are harder than the ones we have had up to now. Don't leave them till the last minute! 1. Find a formula for: n 2 1 8 1 4 1 2 1 + + + + L by examining the values of this expression for small values of n . Prove your result using weak or strong induction. 2. Prove by induction that if n 3, then 2n + 1 < 3n – 1. 3. Consider a game in which two players take turns removing any number of stones from one of two piles (removing all the stones in a pile is allowed). The player who removes the last stone wins the game. Use strong induction to show that if the two piles initially contain the same number of stones, then the second player can always win. 4. Suppose is a partition of a set S. That is, is a set of disjoint, non-empty subsets of S that have S as their union. Define the relation R on S as follows:
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28 PS5 - Handout #28 April 26, 2010 CS103 Robert Plummer...

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