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old-quiz2-solutions - CS 173 Discrete Structures Spring...

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CS 173: Discrete Structures, Spring 2010 Quiz 1 Solutions Notice that the two sections had slightly different versions of many questions, and this document contains solutions to all of them. 1. (1 point) Give the day and time when your assigned discussion section meets. State explicitly if you have switched sections recently. Solution: This obviously varies from person to person. 2. (4 points) Simplify or find the values for the following expression: Solution: log k ( k 2 ) = 2 log k ( k ) = 2 (log k k ) 2 = 1 2 = 1 gcd(42 , 15) = 3 lcm(6 , 21) = 42 3. (4 points) Give a truth table for the following expression and (using your truth table or other means) find a simpler expression equivalent to it. Solution: p ( p q ) = p ( p q ) q = q p q p q p ( p q ) T T T T T F T T F T T F F F F F p q p q ( p q ) q T T T T T F F F F T F T F F F F 1
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4. (4 points) If n k =0 2 k = 2 n +1 1, give a closed-form expression for the following sum- mation. Show your work.
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