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Nested Familiy

  1. Mar 20, 2007 #1
    Hi all,

    Im having trouble with this problem, I dont know where to begin.

    Suppose that Ä is a nested family of sets.

    1. Prove that U (from k=1 to infite) A(sub k) = A(sub l)

    2. Prove that ∩ (from k=1 to n) A(sub k) = A(sub n)


    Thanks in advace mathematicians!

    -William
     
  2. jcsd
  3. Mar 20, 2007 #2
    1) To show that they are equal you must show that they are subsets of one another.

    2) If x is in the union of a collection of sets, what does this mean?

    3) If x is in the intersection of a collection of sets, what does this mean?

    4) You have to use the assumption of nested somewhere.

    5) If A is a subset of B what can you say about A n b?

    6) If A is a subset of B what can you say about A U B?
     
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