For each collection given below, determine whether the sets of the collection ar

Question

For each collection given below, determine whether the sets of the collection are mutually disjoint. Also, determine whether the collection is nested, and find the union and intersection of the collection. (We use interval notation below: (a, b) = {x epsilon R| a

Explanation / Answer

a) (1/n,n+1) = (1,2), (1/2,3), (1/3,4) ... etc Union = (0,+inf), Intersection = (1,2). Sets are nested as (1/n,n+1) (1/m,m+1) for m>n These sets are not mutually disjoint as they have an element namely 1.5 in common. b)(-1/n,n) = (-1,1), (-1/2,2), (-1/3,3) .. etc 0 is a common element of all these sets so they are not mutually disjoint. Union = (-1,+inf), Intersection = (0,1). Sets are not nested. c)Union=(1,+inf), Interection = {} (empty set). Sets are clearly nested. These sets are not mutually disjoint as given any finite collection of sets of C, we can always find a natural number belonging to all these sets. d)Union = R, Intersection = {} (empty set). Sets are clearly nested. These sets are not mutually disjoint as given any finite collection of sets of C, we can always find a real number belonging to all these sets. e)E= (-1,1), (-sqrt(2),sqrt(2)), (-sqrt(3),sqrt(3)) ... etc Union = (-inf,inf)=R, Intersection = (-1,1). Sets are nested. 0 is a common element of all these sets so they are not mutually disjoint. Hope this helped.

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