# Category:Rings of Sets

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This category contains results about **Rings of Sets**.

Definitions specific to this category can be found in Definitions/Rings of Sets.

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: | \(\ds \forall A, B \in \RR:\) | \(\ds A \symdif B \in \RR \) |

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Rings of Sets"

The following 7 pages are in this category, out of 7 total.