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Unformatted text preview: Problem Set 1–Revised 8/2/06, problem 8 Economics 204  August 2006 Due Friday, 4 August in Lecture 1. Set Theory (a) Determine whether this formula is always right or sometimes wrong. Prove it if it is right. Otherwise give both an example and a counterexample and state (but don’t prove) an additional neccesary and suﬃcient condition for it to always be right: A \ ( B \ C ) = ( A \ B ) ∪ C. (b) Certain subsets of a given set S are called Asets and others are called Bsets. Suppose that these subsets are chosen in such a way that the following properties are satisfied: • The union of any collection of Asets is and Aset. • The intersection of any finite number of Asets is an Aset. • The complement of an Aset is a Bset and the complement of a Bset is an Aset. Prove the following: 1. The intersection of any collection of Bsets is a Bset. 2. The union of any finite number of Bsets is a Bset....
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 Summer '08
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 Economics

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