I am wondering if someone could help me with basic properties of semi algebra. We say that $S$ is a semi algebra of subsets of X if
- $\emptyset \in S$
- If $P_1$, $P_2 \in S$, then $P_1 \cap P_2 \in S$
- If $P \in S$, then $X \backslash P$ can be written as a finite union of sets from $S$.
But I am finding that sometimes it is defined using the following 3' instead of 3.
3'. If $P \in S$, then $X \backslash P$ can be written as a disjoint finite union of sets from $S$.
My question is are these definitions equivalent? If so can someone please show me how we can obtain 3' from the first three conditions?