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Math Help - 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 S is a set with n elements (here n=3) then the number subsets of S is 2^n (here 2^3 = 8 so you get eight).
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  3. #3
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    Hello, NeedHelp18!

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

    Answer: . \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 n elements has 2^n subsests.

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



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

    . . \begin{array}{c|c|c}<br />
a & b & c \\ \hline \hline<br />
& &  \\ \hline<br />
& &  \\ \hline<br />
& & \\ \hline<br />
& & \\ \hline<br />
& & \\ \hline<br />
& & \\ \hline<br />
&& \\ \hline<br />
&& \\ \hline  \end{array}


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

    . . \begin{array}{c|c|c}<br />
a & b & c \\ \hline \hline<br />
a & &  \\ \hline<br />
a& &  \\ \hline<br />
a& & \\ \hline<br />
a& & \\ \hline<br />
-& & \\ \hline<br />
-& & \\ \hline<br />
-&& \\ \hline<br />
-&& \\ \hline  \end{array}


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

    . . \begin{array}{c|c|c}<br />
a & b & c \\ \hline \hline<br />
a &b &  \\ \hline<br />
a&b &  \\ \hline<br />
a&- & \\ \hline<br />
a&- & \\ \hline<br />
-&b & \\ \hline<br />
-&b & \\ \hline<br />
-&-& \\ \hline<br />
-&-& \\ \hline  \end{array}


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

    . . \begin{array}{c|c|c}<br />
a & b & c \\ \hline \hline<br />
a &b & c \\ \hline<br />
a&b &-  \\ \hline<br />
a&- &c \\ \hline<br />
a&- &- \\ \hline<br />
-&b &c \\ \hline<br />
-&b &- \\ \hline<br />
-&-&c \\ \hline<br />
-&-&- \\ \hline  \end{array}


    The eight possible subsets appear in the eight rows.

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