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Math Help - Finite math help

  1. #1
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    Finite math help

    List the power set P(S) for the set S = {A,B,C,D,F}?

    24.Describe
    the
    following
    set
    using
    set
    builder
    notation:

    A = {5,15,25,35,45,55,65}
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  2. #2
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    Re: Finite math help

    Quote Originally Posted by iBrute View Post
    List the power set P(S) for the set S = {A,B,C,D,F}?
    I am not sure what the symbol "" means. If a set has n elements, its powerset has 2ⁿ elements. So, P(S) has 32 elements including the empty set, 5 sets containing 1 element each, 10 elements containing 2 elements each, etc. Make sure you understand what a power set is.

    Quote Originally Posted by iBrute View Post
    24.Describe
    the
    following
    set
    using
    set
    builder
    notation:

    A = {5,15,25,35,45,55,65}
    This can be defined as a set of elements of the form 10n + 5 for integer n between 0 and 6.
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  3. #3
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    Re: Finite math help

    As for listing all 2^5= 32 subsets, I recommend starting by listing the "singleton" sets:
    {} (the empty set), {A},{B}, {C},{D}, {F},
    now include each element of the original set "past" that one: {AB}, {AC}, {AD}, {AF}, {BC}, {BD}, {BF}, {CD}, {CF}, {DF}.
    (The point of "past" is to avoid duplicates.)
    Now, add a letter to each of those: {ABC}, {ABD}, {ABF}, {ACD}, {ACF}, {ADF}, {BCD}, {BCF}, {BDF}, {CDF}
    etc.

    As a check, the number of subsets containing n elements is \begin{pmatrix}5 \\ n\end{pmatrix}. So there is \frac{5!}{0!5!}= 1 subset with 0 elements, \frac{5!}{1!4!}= 5 subsets with 1 element, \frac{5!}{2!3!}= 10 subsets with two elements, \frac{5!}{3!2!}= 10 subsets with three elements, \frac{5!}{4!1!}= 5 subsets with 4 elements, and \frac{5!}{5!0!}= 1 subsets with 5 elements (the entire set).

    For {5, 15, 25, 35, 45, 55, 65}, notice that 5= 1(5), 15= 3(5), 25= 5(5), 35= 7(5), 45= 9(5), 55= 11(5), 65= 13(5), odd multiples of 5. And those odd numbers can be written as 2n+1 for n from 0 to 6.
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