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Power Sets

  1. Nov 17, 2012 #1
    While practicing power set problems I came across one that has me stumped.

    The problem asks: Is the following set is a power set of of a set?
    {∅, {b, ∅}, {a}, {a, b}, {b}}

    My answer: This set has 5 elements. Since 5 is not a power of 2, this cannot be the power set of any set.

    The problem then asks: If the set is not a power set of a set, then what is the lacking set?

    This is where I'm stuck. There are no similar problems in the book or on the Internet (that I can find), and I'm not sure how to answer this.

    Thank you for any suggestions!
     
  2. jcsd
  3. Nov 17, 2012 #2

    SammyS

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    If these are elements of the power set of some set, S, start my making a list of the elements of set S.
     
  4. Nov 17, 2012 #3
    Okay if S = {∅, a, b},
    then P(S) = [{∅, {∅}, {a}, {b}, {∅, a}, {∅, b}, {a, b}, {∅, a, b}]
    Thus, the missing sets are {∅}, {∅, a}, and {∅, a, b}.

    Is this correct?
     
    Last edited: Nov 18, 2012
  5. Nov 18, 2012 #4

    SammyS

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    Yes.
     
  6. Nov 18, 2012 #5
    Great! Thanks for the help.
     
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