Definition 13.1.2 (Ring). Let $X$ be a set and $\alg \subset 2^{X}$, then $\alg$ is a ring if:
$\emptyset \in \alg$.
For any $E, F \in \alg$ with $E \subset F$, $F \setminus E \in \alg$.
For any $A, B \in \alg$, $A \cup B \in \alg$.
Definition 13.1.2 (Ring). Let $X$ be a set and $\alg \subset 2^{X}$, then $\alg$ is a ring if:
$\emptyset \in \alg$.
For any $E, F \in \alg$ with $E \subset F$, $F \setminus E \in \alg$.
For any $A, B \in \alg$, $A \cup B \in \alg$.