# Category:Axioms/Ring of Sets Axioms

A system of sets $\RR$ is a ring of sets if and only if $\RR$ satisfies the ring of sets axioms:
 $(\text {RS} 1_1)$ $:$ Non-Empty: $\ds \RR \ne \O$ $(\text {RS} 2_1)$ $:$ Closure under Intersection: $\ds \forall A, B \in \RR:$ $\ds A \cap B \in \RR$ $(\text {RS} 3_1)$ $:$ Closure under Symmetric Difference: $\ds \forall A, B \in \RR:$ $\ds A \symdif B \in \RR$