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Thread: Subsets

  1. #1
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    Subsets

    A = {a, b, c}

    is the answer: A, empty set, {a}, {b}, {c}, {a,b} {b,c} {a,c}
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  2. #2
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    Quote Originally Posted by NeedHelp18 View Post
    A = {a, b, c}

    is the answer: A, empty set, {a}, {b}, {c}, {a,b} {b,c} {a,c}
    Yes

    Here is a good way to check.
    If $\displaystyle S$ is a set with $\displaystyle n$ elements (here $\displaystyle n=3$) then the number subsets of $\displaystyle S$ is $\displaystyle 2^n$ (here $\displaystyle 2^3 = 8$ so you get eight).
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  3. #3
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    Hello, NeedHelp18!

    List the subsets of: .$\displaystyle A \:=\: \{a, b, c\}$

    Answer: .$\displaystyle \emptyset,\; \{a\},\; \{b\},\; \{c\}, \;\{a,b\},\; \{b,c\},\; \{a,c\},\;\{a,b,c\}$ . . . . Right!

    Here's way to ensure that you have all the subsets . . .



    First of all, a set of $\displaystyle n$ elements has $\displaystyle 2^n$ subsests.

    Your set has $\displaystyle n = 3$ elements, so there are $\displaystyle 2^3 = 8$ subsets.



    Make a chart with 8 rows . . . and 3 columns (one for each element).

    . . $\displaystyle \begin{array}{c|c|c}
    a & b & c \\ \hline \hline
    & & \\ \hline
    & & \\ \hline
    & & \\ \hline
    & & \\ \hline
    & & \\ \hline
    & & \\ \hline
    && \\ \hline
    && \\ \hline \end{array}$


    In the first column, write four a's and four blanks.

    . . $\displaystyle \begin{array}{c|c|c}
    a & b & c \\ \hline \hline
    a & & \\ \hline
    a& & \\ \hline
    a& & \\ \hline
    a& & \\ \hline
    -& & \\ \hline
    -& & \\ \hline
    -&& \\ \hline
    -&& \\ \hline \end{array}$


    In the second column, write two b's and two blanks, etc.

    . . $\displaystyle \begin{array}{c|c|c}
    a & b & c \\ \hline \hline
    a &b & \\ \hline
    a&b & \\ \hline
    a&- & \\ \hline
    a&- & \\ \hline
    -&b & \\ \hline
    -&b & \\ \hline
    -&-& \\ \hline
    -&-& \\ \hline \end{array}$


    In the third column, write one c, one blank, etc.

    . . $\displaystyle \begin{array}{c|c|c}
    a & b & c \\ \hline \hline
    a &b & c \\ \hline
    a&b &- \\ \hline
    a&- &c \\ \hline
    a&- &- \\ \hline
    -&b &c \\ \hline
    -&b &- \\ \hline
    -&-&c \\ \hline
    -&-&- \\ \hline \end{array}$


    The eight possible subsets appear in the eight rows.

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