# Definition:Ring of Sets/Definition 2

A ring of sets $\RR$ is a system of sets with the following properties:
 $(\text {RS} 1_2)$ $:$ Empty Set: $\ds \O \in \RR$ $(\text {RS} 2_2)$ $:$ Closure under Set Difference: $\ds \forall A, B \in \RR:$ $\ds A \setminus B \in \RR$ $(\text {RS} 3_2)$ $:$ Closure under Union: $\ds \forall A, B \in \RR:$ $\ds A \cup B \in \RR$