Definition:Ring of Sets/Definition 2

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Definition

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

\((\text {RS} 1_2)\)   $:$   Empty Set:    \(\ds \O \in \RR \)             
\((\text {RS} 2_2)\)   $:$   Closure under Set Difference:      \(\ds \forall A, B \in \RR:\) \(\ds A \setminus B \in \RR \)             
\((\text {RS} 3_2)\)   $:$   Closure under Union:      \(\ds \forall A, B \in \RR:\) \(\ds A \cup B \in \RR \)             


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