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

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
COT 3100 Final Exam Spring 2001 TA : _______________ Section # : __________ Name : _____________ 4/26/01
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
1) (15 pts) Use induction to prove that 64 | (3 2n – 8n – 1) for all integers n 0.
Background image of page 2
2) (10 pts) Let c be an integer such that 3 | c. Prove that (c+1) 3 1 (mod 9).
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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|.
Background image of page 4
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.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
7) (15 pts) Use induction on n to prove the following inequality for all positive integers n:
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 12

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online