Category:Rings of Sets

This category contains results about Rings of Sets.
Definitions specific to this category can be found in Definitions/Rings of Sets.

A ring of sets $\RR$ is a system of sets with the following properties:

$(\text {RS} 1_1)$	$:$	Non-Empty:		$\displaystyle \RR \ne \O $
$(\text {RS} 2_1)$	$:$	Closure under Intersection:	$\displaystyle \forall A, B \in \RR:$	$\displaystyle A \cap B \in \RR $
$(\text {RS} 3_1)$	$:$	Closure under Symmetric Difference:	$\displaystyle \forall A, B \in \RR:$	$\displaystyle A * B \in \RR $

Subcategories

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

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

\((\text {RS} 1_1)\)	$:$	Non-Empty:		\(\displaystyle \RR \ne \O \)
\((\text {RS} 2_1)\)	$:$	Closure under Intersection:	\(\displaystyle \forall A, B \in \RR:\)	\(\displaystyle A \cap B \in \RR \)
\((\text {RS} 3_1)\)	$:$	Closure under Symmetric Difference:	\(\displaystyle \forall A, B \in \RR:\)	\(\displaystyle A * B \in \RR \)