Definition:Algebra of Sets/Definition 1

Definition
Let $X$ be a set.

Let $\mathcal P \left({X}\right)$ be the power set of $X$.

Let $\mathcal R \subseteq \mathcal P \left({X}\right)$ be a set of subsets of $X$.

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

Also see

 * Equivalence of Definitions of Algebra of Sets