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Unformatted text preview: MATH 240; EXAM # 2, 100 points, November 21, 2006 (R.A.Brualdi) TOTAL SCORE (7 problems; 100 points possible): Name: These R. Solutions TA: Luanlei Zhao (circle time) Mon 9:55 — Mon 11:00 — Wed 9:55 — Wed. 11:00 1. [14 points] Give a recursive definition with initial conditions of the following function and set: (a) If a 1 , a 2 , . . ., a n , . . . is an infinite sequence, then for n ≥ 1, f ( n ) = a 1 + a 2 + · · · + a n (the n th partial sum). f ( n ) = f ( n 1) + a n , ( n ≥ 2) , f (1) = a 1 . (b) The set A of bit sequences of any length at least 1 such that the sequence does not contain two consecutive 0’s. 1 , , 01 , 10 , 11 are in A ; if a 1 a 2 . . .a n 1 1 is in A then so is a 1 a 2 . . .a n 1 0 and a 1 a 2 . . .a n 1 1; if a 1 a 2 . . .a n 1 0 is in A then so is a 1 a 2 . . .a n 1 01. 2. [5 points] Compute the following Boolean product : bracketleftBigg 1 0 1 0 1 1 bracketrightBigg circledot 0 1 1 1 1 0 = bracketleftBigg 1 1 1 1 bracketrightBigg ....
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This note was uploaded on 08/11/2008 for the course MATH 240 taught by Professor Miller during the Fall '08 term at University of Wisconsin.
 Fall '08
 Miller
 Math

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