CS 162 - Algorithms Homework 6, 25 Points
Due: Second Lecture of WEEK 7, 10 minutes before class starts.
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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.
-
5 points.
Exercise 4.8 from Sipser.
-
5 points.
Problem 4.21 from Sipser.
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5 points.
Problem 5.9 from Sipser.
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5 points.
Problem 5.30b from Sipser. (Hint: Use the answer for 5.30a as a template.)