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Note: You are looking at a static copy of the former PineWiki site, used for class notes by James Aspnes from 2003 to 2012. Many mathematical formulas are broken, and there are likely to be other bugs as well. These will most likely not be fixed. You may be able to find more up-to-date versions of some of these notes at http://www.cs.yale.edu/homes/aspnes/#classes.

Here are the /Solutions.

This assignment is due Tuesday, September 13th, 2005 at 11:00pm. For due dates of future assignments, see CS202/Assignments.

1. Bureaucratic part

This part you will not be graded on, but you should do it anyway.

Send me email. My address is <aspnes@cs.yale.edu>. In your message, include:

  1. Your name.
  2. Your status: whether you are an undergraduate, grad student, auditor, etc.
  3. Which course you are taking.

  4. Whether you have ever taken a class that used Grade-o-Matic before.1

  5. Anything else you'd like to say.

2. Technical part

This part you will be graded on.

  1. Prove or disprove: (p \/ q) => (q \/ r) is logically equivalent to (p \/ ¬q) => r.

  2. Prove or disprove: for all natural numbers n, n2+2n is a multiple of 3.

  3. Prove or disprove: for all natural numbers n, n3+2n is a multiple of 3.

  4. Prove or disprove: for all sets A and B, ∅∈A => ∅⊆B.

  5. Prove by induction on n that, for any real number x ≥ -1 and any integer n ≥ 1, (1+x)n ≥ 1 + nx. (Hint: use the fact that a ≥ 0 and b ≥ c implies ab ≥ ac, where a, b, and c are all real numbers.)

Clarification added 2005-09-06: for problems 2 and 3, you should assume that 0 is a natural number (and that it is a multiple of 3).

  1. Ulterior motive: The information in your email will be used to create an account for you in Grade-o-Matic. (1)

2014-06-17 11:57