Definition 17.1.2 (Ring).label Let $X$ be a set and $\alg \subset 2^{X}$, then $\alg$ is a ring if:

1. (A1)

   $\emptyset \in \alg$.

2. (A2’)

   For any $E, F \in \alg$ with $E \subset F$, $F \setminus E \in \alg$.

3. (A3)

   For any $A, B \in \alg$, $A \cup B \in \alg$.