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Unformatted text preview: CS 2800 – Fall 2008 Review Problems for the Final 1. Convert the following statements into propositional logic and determine if the given argument is sound: Rainy days make gardens grow. Gardens don’t grow if it is not hot. It always rains on a day that is not hot. Therefore, if it is not hot, then it is hot. 2. We define the set S = { x  x / ∈ S } . Does S ∈ S ? Does S / ∈ S ? 3. Show that if A and B are countable sets, then A × B is also countable. 4. Show that the power set of the set of positive integers Z + is uncountable. 5. What is the best bigO function for (a) n 3 + sin n 7 (b) ( x + 2) log 2 ( x 2 + 1) + log 2 ( x 3 + 1) 6. What is the worstcase time complexity of the following algorithms? (a) One that prints out all the ways to place the numbers 1 , 2 ,...,n in a row. (b) One that enumerates all the subsets of a given finite set of size n . 7. Prove that if n is an integer that is not a multiple of 3, then n 2 ≡ 1 (mod 3)....
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This note was uploaded on 10/04/2010 for the course CS 2800 at Cornell.
 '07
 SELMAN

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