# HW4 - State your proof strategy at the beginning 4(6 points...

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EECS 203: DISCRETE MATHEMATICS Homework 4 Due Thursday, October 4 at 4pm Put your name and discussion section number (not the meeting time) on the ﬁrst page of your homework. Submit your homework to (a) CTools, as a PDF ﬁle, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (8 points) Chapter 2.3, Problem 18. Explain your answer to each part. 2. (6 points) Prove that if three people have appeared in the same movie and one has a Bacon number then two have the same Bacon number. State your proof strategy at the beginning. 3. (6 points) The people p 1 , p 2 , p 3 , . . . , p n form a cycle if p 1 and p n have been in a movie together and, for all i in the range 1 i n - 1, p i and p i +1 have been in a movie together. Prove that if p 1 , . . . , p n form a cycle, n 3, and one of them has a Bacon number then two people have the same Bacon number.
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Unformatted text preview: State your proof strategy at the beginning. 4. (6 points) A Japanese restaurant sells a 6-piece sushi combo, a 9-piece combo, and a 20-piece combo. The number of individual pieces of sushi that can be ordered are called sushi numbers , which are of the form: c 1 · 6 + c 2 · 9 + c 3 · 20 where c 1 , c 2 , c 3 ∈ N are the number of 6-piece, 9-piece, and 20-piece combos that are ordered. There are clearly an inﬁnite number of sushi numbers. Prove that there are a ﬁnite number of natural numbers that are not sushi numbers. State your proof strategy at the beginning. 5. (6 points) Recall that two (possibly inﬁnite) sets A and B are deﬁned to be the same size if there is a bijection f : A → B . Show that Z + (positive integers) and Z (integers) have the same size. 6. (0 points) Show that R + (positive reals) and R (reals) have the same size. 1...
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