The set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ can be written in set-builder notation as:

$\{ x \mid x \in \mathbb{Z}, 1 \leq x \leq 12 \}$

This describes the set of integers $x$ such that $x$ is between 1 and 12, inclusive.

Do you want details on how set-builder notation works or any other clarifications?

Here are 5 related questions to consider:

1. How can set-builder notation be used to describe more complex sets?
2. What is the difference between set-builder and interval notation?
3. How would you describe a set of even numbers within this range in set-builder notation?
4. Can set-builder notation be used to represent an infinite set?
5. How do you denote a set that excludes specific values using set-builder notation?

Tip: When using set-builder notation, always clearly define the condition that elements must satisfy.