(7.1)--7.1-NestofSets.pdf

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1、7.17.1 Nest of SetsNest of Sets Example 1Example 1 Let Let .Let.Let:,where where ,.By By resolution principle resolution principle,if,if,then ,then .,Nest of Nest of setssets Let Let:,.is called is called a nest a nest of of sets sets in in if if,.The collection of sets The collection of sets ,is al

2、so called is also called a a nest of sets nest of sets in in.The The set of all the set of all the nests nests of sets of sets in in is denoted by is denoted by .Example 2 Example 2 Let Let .a)a)Determine Determine whether whether ,is a nest of setsis a nest of sets.b)b)Determine whetherDetermine wh

3、ether ,is a nest of sets.is a nest of sets.c)c)Let Let ,where where ,.Determine whether.Determine whether ,is a nest of sets.is a nest of sets.Operations on the nests of sets Operations on the nests of sets Union Union IntersectionIntersection ComplementationComplementation Let Let,.is called the is

4、 called the unionunion of of and and,wherewhere ()=,.is called the is called the intersectionintersection of of and and,where where ()=,.Analysis Analysis Let Let,.,()(),.Let Let be an identifier set,be an identifier set,.is called the is called the unionunion of of|where where =,.is called the is c

5、alled the intersectionintersection of of|where where =,.Analysis Analysis Let Let .If If werewere defined as followsdefined as follows,=,.ComplementationComplementation Let Let .is called is called the complement of the complement of,where where =，,.=,.Suppose Suppose .ConclusionConclusion Suppose Suppose,.Then.Then ,.Let Let be be an identifier an identifier set.Suppose set.Suppose ,.Then.Then ,.