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 $\displaystyle S$ 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).

3. 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.