Definition:Ring of Sets/Definition 3

A system of sets $\RR$ is a ring of sets if and only if $\RR$ satisfies the ring of sets axioms:
 $(\text {RS} 1_3)$ $:$ Empty Set: $\ds \O \in \RR$ $(\text {RS} 2_3)$ $:$ Closure under Set Difference: $\ds \forall A, B \in \RR:$ $\ds A \setminus B \in \RR$ $(\text {RS} 3_3)$ $:$ Closure under Disjoint Union: $\ds \forall A, B \in \RR:$ $\ds A \cap B = \O \implies A \cup B \in \RR$