The operations of set union and set intersection can be

Chapter 4, Problem 93

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The operations of set union and set intersection can be extended to apply to an infinite family of sets. We may describe the family as the collection of all sets Ai , where i takes on any of the values of a fixed set I. Here, I is called the index set for the family. The union of the family, di[I Ai, is defined by di[I Ai = {x 0 x is a member of some Ai } The intersection of the family, ti[I Ai, is defined by ti[I Ai = {x 0 x is a member of each Ai }. a. Let I = {1, 2, 3, }, and for each i [ I, let Ai be the set of real numbers in the interval (1/i, 1/i). What is di[I Ai? What is ti[I Ai? b. Let I = {1, 2, 3 }, and for each i [ I, let Ai be the set of real numbers in the interval [1/i, 1/i]. What is di[I Ai? What is ti[I Ai?