# Homework Assignment #5

#### Problem 6.4.1 corrected 4 November 2004.

There are nine questions for 100 total points. All are from the textbook, A Mathematical Foundation for Computer Science, from the green (4-5) and yellow (6-7) volumes. "Problem 1.1.2", for example, refers to Problem #2 in Section 1.1, and similarly. Make sure you don't do an Exercise when a Problem is assigned!

• Page 5-10: Problem 5.2.4 (10)

• Page 5-15: Problem 5.4.2 (10) Correction: The statement you are asked to prove in the text is false. (For example, let S = aa and T = aaaa.) Instead, please prove the following for a one-letter alphabet: If S and T are any regular expressions, then (S+T)* = S*T*.

• Page 5-22: Problem 5.5.1 (15)

• Pages 6-8 and 6-9: Problems 6.1.2 (10) and 6.1.5 (10)

• Page 6-14: Problem 6.2.1 (10)

• Page 6-18: Problem 6.3.4 (15)

• Page 6-23: Problem 6.4.1 (10) Correction (4 Nov): The "j-k falling" at the very end of the problem should read "k-j falling".

• Page 6-33: Problem 6.6.3 (10)