The number of subsets of a given set is determined by the formula:

$\text{Number of subsets} = 2^n$

where $n$ is the number of elements in the set.

For the set $\{12, 11, 7\}$, there are 3 elements. Using the formula:

$2^3 = 8$

Thus, the set $\{12, 11, 7\}$ has 8 subsets.

These subsets are:

1. $\emptyset$ (the empty set)
2. $\{12\}$
3. $\{11\}$
4. $\{7\}$
5. $\{12, 11\}$
6. $\{12, 7\}$
7. $\{11, 7\}$
8. $\{12, 11, 7\}$

Would you like more details or have any other questions?

Here are 5 related questions to further your understanding:

1. How many subsets does a set with 5 elements have?
2. What is the number of non-empty subsets of a set with 4 elements?
3. Can you find the number of subsets of the set $\{1, 2, 3, 4, 5\}$?
4. How many subsets does the empty set have?
5. How does the concept of a power set relate to the number of subsets?

Tip: The total number of subsets always includes the empty set and the set itself.