Definition 13.1.1 (Algebra). Let $X$ be a set and $\alg \subset 2^{X}$, then $\alg$ is an algebra if:
$\emptyset, X \in \alg$.
For any $A \in \alg$, $A^{c} \in \alg$.
For any $A, B \in \alg$, $A \cup B \in \alg$.
Definition 13.1.1 (Algebra). Let $X$ be a set and $\alg \subset 2^{X}$, then $\alg$ is an algebra if:
$\emptyset, X \in \alg$.
For any $A \in \alg$, $A^{c} \in \alg$.
For any $A, B \in \alg$, $A \cup B \in \alg$.