Axiom:Ring of Sets Axioms/Axioms 3

Definition

Let $\RR$ be a system of sets.

$\RR$ is a ring of sets if and only if $\RR$ satisfies the following axioms:

\((\text {RS} 1_3)\)	$:$		Empty Set:		\(\ds \O \in \RR \)
\((\text {RS} 2_3)\)	$:$		Closure under Set Difference:	\(\ds \forall A, B \in \RR:\)	\(\ds A \setminus B \in \RR \)
\((\text {RS} 3_3)\)	$:$		Closure under Disjoint Union:	\(\ds \forall A, B \in \RR:\)	\(\ds A \cap B = \O \implies A \cup B \in \RR \)

These criteria are called the ring of sets axioms.

Also see

• Definition:Ring of Sets/Definition 3

• Equivalence of Definitions of Ring of Sets