# FinalExam - COT 3100 Final Exam Spring 2001 TA Section Name...

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COT 3100 Final Exam Spring 2001 TA : _______________ Section # : __________ Name : _____________ 4/26/01

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1) (15 pts) Use induction to prove that 64 | (3 2n – 8n – 1) for all integers n 0.
2) (10 pts) Let c be an integer such that 3 | c. Prove that (c+1) 3 1 (mod 9).

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3) (7 pts) Draw a DFA to accept the language of strings over the alphabet {a,b} that contain an odd number of a’s and an even number of b’s. (Please use only four states when drawing this DFA.) 4) (10 pts) Given sets A, B and C, we have the following information: i) |C| = 10 ii) |A B| = 12 iii) |(A B) C| = 4 Find |A B C|.
5) (5 pts) Find the regular expression over the alphabet {0,1} of all binary strings whose value is divisible by 8. (Note: Do not include λ in this language. But do include strings with any number of leading 0’s.) 6) (5 pts) Find the regular expression for all strings over the alphabet {x,y,z} that contain at most two distinct characters.

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7) (15 pts) Use induction on n to prove the following inequality for all positive integers n:
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FinalExam - COT 3100 Final Exam Spring 2001 TA Section Name...

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