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Unformatted text preview: Answer key of First Midterm Examination, Math 61, Version 1 1 . Compute the following numbers, explain how you get the answer and write your answer in the following boxes as indicated: a. 60 b. 62 c. 4 d. 32 e. 18 a. In a seven person committee made of persons A,B,C,D,E,F,G , in how many ways can we select a chairperson, secretary and treasurer if either A or B must be chairperson? The number of committee choice with chair person A: P (6 , 2) = 30, The number of committee choice with chair person B: P (6 , 2) = 30, Thus the answer = 30 + 30 = 60. b. How many 6-bit strings have at least one set of consecutive “00” or “11”? 6-bit strings without consecutive 00 or 11 are 101010 and 010101. Thus the total is 2 6 − 2 = 64 − 2 = 62. c. In the set of eight bit strings, x and y are defined to be related if first 6 bits of x and y coincide. How many elements in an equivalence classe are there?...
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- Spring '08
- Equivalence relation, equivalence class, Congruence relation, Partition of a set