ECE-103-1029-Final_exam

ECE-103-1029-Final_exam - FINAL EXAMINATION FALL TERM 2002...

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FINAL EXAMINATION FALL TERM 2002 QUESTION 1. (a) [3] Prove or disprove: in a nonempty universe of dis- course, ( x y P ( x, y )) ( y x P ( x, y )) . (b) [5] Let a n be defined by a 0 = 1 and, for n 1, a n = a n - 1 + 5. Prove n 0, a n (1 + 21) / 2. QUESTION 2: [5] Find all solutions to 15 x + 65 y = 150. QUESTION 3: A standard deck of cards has 52 cards, 13 in each of four suits. (a) [5] What is wrong with the following argument that “shows” there are 4 39 13 ways to select 13 cards from the 52 so that at least one suit has no cards among the 13 selected. “For any specific one of the suits, there are 39 cards not in that suit. Thus, there are 39 13 ways of selecting 13 cards so that none are in the specific suit. Since there are 4 ways of selecting the specific suit, there are 4 39 13 ways of selecting 13 cards so that at most three suits appear among the selected cards.” (b) [5] Give a correct count for the number of ways of selecting 13 cards from the standard deck so that at most three suits appear among the selected cards.
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