Axiom:Ring of Sets Axioms/Axioms 1

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Let $\RR$ be a system of sets.

$\RR$ is a ring of sets if and only if $\RR$ satisfies the following 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:      \(\ds \forall A, B \in \RR:\) \(\ds A \symdif B \in \RR \)      

These criteria are called the ring of sets axioms.

Also see