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Subset and proper subset

  1. Jun 20, 2008 #1
    Let 's Consider a set A where A={1,2,3}

    Can anyone tell me
    1>no of subsets of A
    2>no of proper subsets of A

    Regards,
    Asit
     
  2. jcsd
  3. Jun 20, 2008 #2
    What have you tried already? If you know the definition of subset, it should be easy enough to make a list of all the subsets and then count them. There is also a very simple formula relating the number of subsets of a given set to its cardinality.

    After you answer part 1, part 2 is simply the number of subsets of A minus the number of those sets which are not proper subsets. (what is the definition of proper subset?)
     
  4. Jun 20, 2008 #3
    i know the asnwer

    if A has three elements, proper subset of A will be 7
    becoz all the subsets will be Null,{1},{2},{3},{1,2},{2,3},{1,3}
    subsets of A will be 8 BY INCLUDING {1,2,3}

    I asked it, becoz i m not sure ab it.

    Am i correct ab it ??
     
  5. Jun 20, 2008 #4
    the formula for the cardinality of the powerset is 2^(cardinality of the set) hence the number is 8 not 7
     
  6. Jun 21, 2008 #5
    i m saying ab proper subset not subset....
     
  7. Jun 21, 2008 #6
    Yes, that's correct.
     
  8. Jun 22, 2008 #7

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If a set, A, contains n members, then it has 2n subsets. Since that includes A itself, which is not a proper subset of itself, A has 2n-1 proper subsets. (And A has 2n-2 proper, nonempty subsets.)
     
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