Definition:Algebra of Sets/Definition 1

Definition
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 $A, B \in \mathcal S$:


 * $(1): \quad A \cup B \in \mathcal S$
 * $(2): \quad \complement_X \left({A}\right) \in \mathcal S$

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

Also see

 * Equivalence of Definitions of Algebra of Sets