CS 162 - Algorithms Homework 6, 25 Points
Due: Second Lecture of WEEK 7, 10 minutes before class starts.

  1. 5 points. Show, by a diagonalization argument, that the power set of all positive integers is uncountable. Recall that the power set (denoted as P(Z) or as 2Z) of a set, Z, is the collection of all possible subsets of Z. Thus, you need to show that there are an uncountable number of subsets of the positive integers.
  2. 5 points. Exercise 4.8 from Sipser.
  3. 5 points. Problem 4.21 from Sipser.
  4. 5 points. Problem 5.9 from Sipser.
  5. 5 points. Problem 5.30b from Sipser. (Hint: Use the answer for 5.30a as a template.)