Definition:Ring of Sets

A ring of sets $$\mathcal {R}$$ is a non-empty system of sets such that for all $$A, B \in \mathcal {R}$$: where $$\cup$$ denotes set intersection and $$*$$ denotes set symmetric difference.
 * $$A \cap B \in \mathcal{R}$$;
 * $$A * B \in \mathcal{R}$$