Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  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


    User Avatar
    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.)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook