Definition:Ring of Sets/Definition 2

Definition
A ring of sets $\mathcal R$ is a system of sets such that for all $A, B \in \mathcal R$:
 * $(1)': \quad \varnothing \in \mathcal R$
 * $(2)': \quad A \setminus B \in \mathcal R$
 * $(3)': \quad A \cup B \in \mathcal R$

where $\cup$ denotes set union and $\setminus$ denotes set difference.

That is, the operations $\cup$ and $\setminus$ are closed in $\mathcal R$.

Also see

 * Equivalence of Definitions of Ring of Sets