Definition:Ring of Sets/Definition 1

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 $

\((\text {RS} 1_1)\)	$:$	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:	\(\ds \forall A, B \in \RR:\)	\(\ds A \symdif B \in \RR \)