204ps12006 - Problem Set 1–Revised problem 8 Economics...

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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 A-sets and others are called B-sets. Suppose that these subsets are chosen in such a way that the following properties are satisfied: • The union of any collection of A-sets is and A-set. • The intersection of any finite number of A-sets is an A-set. • The complement of an A-set is a B-set and the complement of a B-set is an A-set. Prove the following: 1. The intersection of any collection of B-sets is a B-set. 2. The union of any finite number of B-sets is a B-set....
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204ps12006 - Problem Set 1–Revised problem 8 Economics...

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