\begin{definition}[Definition:Ring of Sets/Definition 1]
A '''ring of sets''' $\RR$ is a system of sets with the following properties:
{{begin-axiom}}
{{axiom | n = \text {RS} 1_1
        | lc= Non-Empty:
        | m = \RR \ne \O
}}
{{axiom | n = \text {RS} 2_1
        | lc= Closure under Intersection:
        | q = \forall A, B \in \RR
        | m = A \cap B \in \RR
}}
{{axiom | n = \text {RS} 3_1
        | lc= Closure under Symmetric Difference:
        | q = \forall A, B \in \RR
        | m = A \symdif B \in \RR
}}
{{end-axiom}}
\end{definition}