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Thread: Number of sets to write

  1. #1
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    Number of sets to write

    Set A= {a,b,c,d,e}
    A U B = {a,b,c,d,e,f,g,h,k,m,n}
    Based on this, how many different sets of B can be written ?
    I tried 2^6 or 6! But it says answer is 32... why is that ?
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  2. #2
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    Re: Number of sets to write

    Quote Originally Posted by ketanco View Post
    I tried 2^6 or 6! But it says answer is 32... why is that ?
    2^6 = 64, 6! = 720
    Any reason you "tried" these?
    Interestingly: 2^5 = 32.
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  3. #3
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    Re: Number of sets to write

    Quote Originally Posted by ketanco View Post
    Set A= {a,b,c,d,e}
    A U B = {a,b,c,d,e,f,g,h,k,m,n}

    Based on this, how many different sets of B can be written ?
    I tried 2^6 or 6! But it says answer is 32... why is that ?
    Set A doesn't have any of the (last visually listed as above) elements in it, so you're going to have to union {f, g, h, k, m, n}
    with every subset of set A down to the empty set to get every different possible set B.


    {a,b,c,d,e} U {f, g, h, k, m, n}
    .
    .
    .

    { } U {f, g, h, k, m, n}


    There are $\displaystyle \ 2^5 \ = \ 32 \ $ of these.
    Last edited by greg1313; Nov 14th 2018 at 08:38 AM.
    Thanks from DenisB
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