\begin{definition}[Definition:Algebra of Sets/Definition 1]
Let $X$ be a set.
Let $\powerset X$ be the power set of $X$.
Let $\RR \subseteq \powerset X$ be a set of subsets of $X$.
Then $\RR$ is an '''algebra of sets over $X$''' {{iff}} the following conditions hold:
{{begin-axiom}}
{{axiom | n = \text {AS} 1
        | lc= Unit:
        | m = X \in \RR
}}
{{axiom | n = \text {AS} 2
        | lc= Closure under Union:
        | q = \forall A, B \in \RR
        | m = A \cup B \in \RR
}}
{{axiom | n = \text {AS} 3
        | lc= Closure under Complement Relative to $X$:
        | q = \forall A \in \RR
        | m = \relcomp X A \in \RR
}}
{{end-axiom}}
\end{definition}