# Thread: Subsets

1. ## Subsets

A = {a, b, c}

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

2. Originally Posted by NeedHelp18
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).

3. 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).

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

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

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

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

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

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

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

The eight possible subsets appear in the eight rows.