8 More on Operations on Sea 88 Problem 8. A collection of sets d is said to be p

Question

8 More on Operations on Sea 88 Problem 8. A collection of sets d is said to be pairwise disjoint if the foll ing is satisfied: For all X,Y Ed, if X nY 0, then X Y informally, a collec A comment about this definition may be in order: Speaking tion of sets is pairwise disjoint if whenever we choose two sets from the collectio they are disjoint or they are equal (a) Give an example of a pairwise di collection of infinitely many sets (c) What is the converse of "if xnY 0, then X Y"? (d) If s is a pairwise disjoint collection of sets, does the assertion you found in (b) hold for all X,Y E s? (e) If the assertion that you found in (b) holds for all X and Y in some set d,is a pairwise disjoint collection of sets? (f Suppose that B is a pairwise disjoint collection of sets. Can we conclude that (g) Suppose that nxeax 0. Is necessarily a pairwise disjoint collection of sets? Problem 8.19. For n E N we define An txEN i We use these sets for two collections of sets: :n e N) and HAA?n denotes the set of even nonnega i Chapte The P Now tha even m sets: the of two

Explanation / Answer

Example:Let S1 = {x| 0<x<1} a subset of R Let S2 = {x| 1<x<2} a subset of R Let S3 = {x| 2<x<3} a subset of R etc so for each positive integer n, Sn = {x| n-1<x<n} a subset of R. Then G = {S1, S2, S3, ...} is an infinite collection of pairwise disjoint subsets of R.

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