To determine the possible subsets of the set $\{0, 1, 2\}$, we can follow the rule that the number of subsets of a set with $n$ elements is given by $2^n$.

In this case, the set $\{0, 1, 2\}$ has 3 elements, so the number of possible subsets is: $2^3 = 8$

Here are the 8 possible subsets of $\{0, 1, 2\}$:

1. $\emptyset$ (the empty set)
2. $\{0\}$
3. $\{1\}$
4. $\{2\}$
5. $\{0, 1\}$
6. $\{0, 2\}$
7. $\{1, 2\}$
8. $\{0, 1, 2\}$

These are all the subsets, including the empty set and the set itself.

Would you like more details or clarification on how subsets work?

Here are 5 related questions to explore further:

1. How many subsets does a set with 5 elements have?
2. What is the difference between a subset and a proper subset?
3. How do you determine the number of proper subsets of a set?
4. What is a power set, and how is it related to subsets?
5. Can subsets contain repeated elements?

Tip: The empty set $\emptyset$ is always a subset of any set, no matter its size.