Definition (Ring of sets)

A ring of sets $\mathscr{A}\subset\mathcal{P}(X)$ is a collection of sets such that

1. $\emptyset\in\mathscr{A}$
2. $A,B\in\mathscr{A}\implies A\cup B\in\mathscr{A}$
3. $A,B\in\mathscr{A}\implies A\setminus B\in\mathscr{A}$