Definition:Ring of Sets/Definition 1
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Definition
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: | \(\ds \forall A, B \in \RR:\) | \(\ds A \symdif B \in \RR \) |