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Unformatted text preview: MAD 2104 Oct 13, 2011 Quiz 4 Key Prof. S. Hudson 1) [30pts] Show that the union of two countable sets is always countable. As usual, a large part of your grade will be based on your explanation (use enough words!). 2) [20pts] How many bit strings are there of length 5 or less ? 3) [20pts] Compute the Boolean product A B , where A = 1 0 1 1 0 0 and B = 1 1 0 0 1 1 4) [30pt] Choose ONE proof. Use induction. You may answer on the back. a) Prove for every positive integer n , that 1 2 + 2 2 + ··· + n 2 = n ( n + 1)(2 n + 1) / 6. b) Prove for every positive integer n , that 3 divides n 3 n . Remarks and Answers: The average of the top 20 grades was approx 74 / 100. The lowest grades were mostly on Problem 1, but the rest were OK on average. The scale is A’s 82  100 B’s 72  81 C’s 62  71 D’s 52  61 As on Quiz 3, I have estimated your semester grade in the upper right corner. But this time, I added your best 3 out of 4 quiz grades, so far. The average for this was about 240time, I added your best 3 out of 4 quiz grades, so far....
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This note was uploaded on 12/27/2011 for the course MAD 2104 taught by Professor Staff during the Fall '08 term at FIU.
 Fall '08
 STAFF

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