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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 < b in L . 1...
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- Fall '09