# Category:Axioms/Ring of Sets Axioms

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This category contains axioms related to 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: | \(\ds \forall A, B \in \RR:\) | \(\ds A \symdif B \in \RR \) |

## Pages in category "Axioms/Ring of Sets Axioms"

The following 4 pages are in this category, out of 4 total.