Definition:Algebra of Sets/Definition 1

Definition
Let $X$ be a set.

Let $\powerset X$ be the power set of $X$.

Let $\mathcal R \subseteq \powerset X$ be a set of subsets of $X$.

Then $\mathcal R$ is an algebra of sets over $X$ the following conditions hold:

Also see

 * Equivalence of Definitions of Algebra of Sets