# hw2 - 0 acquaintances. Nobody is an acquaintance o...

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HOMEWORK #2, DUE ON 9/13 (1) Let k be an arbitrary positive integer. Prove that k has a multiple in which all decimal digits are either 0 or 1. (2) The Fibonacci sequence is defned as a 1 = 1, a 2 = 1, and a i = a i - 1 + a i - 2 ±or all i 3. Show that among the frst 100 million elements, at least one is divisible by 10000. (3) (Exercise 17 o± Chapter 3) There are 100 people at a party. Each person has an even number o± acquaintances. Prove that there are three people at the party with the same number o± acquaintances. Notes: people may have
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Unformatted text preview: 0 acquaintances. Nobody is an acquaintance o himsel/hersel. Acquain-tanceship is a symmetric relation. (4) Prove that the intersection R S o two partial orders on a set X is also a partial order on X . Is the union o two partial orders on X always a partial order? (5) (Exercise 54 o Chapter 4) Let ( X, ) be a fnite partially ordered set. Let a and b be incomparable elements o X . Show that ( X, ) has a linear extension L such that a &lt; b in L . 1...
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