Axiom:Ring of Sets Axioms/Axioms 3

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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:

\((\text {RS} 1_3)\)   $:$   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:      \(\ds \forall A, B \in \RR:\) \(\ds A \cap B = \O \implies A \cup B \in \RR \)      

These criteria are called the ring of sets axioms.

Also see