Definition:Algebra of Sets

Given a set $$X \ $$ and a collection of subsets of $$X \ $$, $$\mathcal{S} \subset \mathcal{P} \left({X}\right) \ $$, $$\mathcal{S} \ $$ is called an algebra of sets if, given that $$A, B \in \mathcal{S} \ $$,


 * 1) $$A \cup B \in \mathcal{S} \ $$
 * 2) $$\mathcal{C}_X \left({A}\right) \in \mathcal{S} \ $$

where $$\mathcal{C}_X \left({A}\right)$$ is the relative complement of $$A \ $$ in $$X$$.