How do you do interval notation?

\(x\in (a, b)\implies a < x < b\\ x \in (a, b] \implies a < x \le b\\ x \in [a, b) \implies a \le x < b\\ x \in [a,b] \implies a \le x \le b\)

\(\cup\text{ means or}\\ \cap\text{ means and}\)

arnt those things union and intersection?

Yes. Glad you know these.

The union of few intervals means that x satisfies any of them, so it means "or".

The intersection of few intervals means that x must satisfy all of them, so it means "and".

:O that is a mouthful