Homework 4: Due *Monday*, October 29, at *2pm*.
(See the class webpage for how to drop off your homeworks.)

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Section 3.6 [These are questions postponed from hmw3]:
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2, 4, 12, 6, 8 [note the reversed order, i.e. do 12 first]
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20 [algorithm 5 in the book is slightly different from the "square and multiply" algorithm in the lecture notes:  you can use *either one* of these two algorithms to compute this, because they compute the same answer using the same number of squarings and multiplications.  it's just that they do it in a different order.]
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Section 4.1:
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What's the size of the power set P(S) in terms of the size of set S?
Prove your claim by induction on the size of S.
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From the book:  Do exercises 4, 6, 10, 18, 40, 56, 60 [in problem 60 please prove it only for n>=2, i.e. use n0 = 2 as a base point.  this way you can avoid certain logical mistake that I think some of you could easily made otherwise....]
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In all problems for inductive proofs it's a good idea that you clearly state two things at the beginning of your solution to the problem:
First, what's the predicate P(n) that you'll be proving.  Second, what's the base case, n0, that you need to show this for.  And then clearly mark in your solution two
parts of the inductive proof:  The base part, where you show that P(n0) is true, and the inductive part, where you show that for all n>=n0 the *implication* (P(n)=>P(n+1)) is true.