If a set $X$ is disjoint, the union of $X$ is called a disjoint union. The notation
\[A = \bigsqcup X\]means
\[A = \bigcup X \enspace\land\enspace \text{$X$ is disjoint}.\]For any sets $X_1$, $\cdots$, $X_n$ ($n \geq 2$), we write
\[X_1 \sqcup \cdots \sqcup X_n = \bigsqcup \{X_1, \cdots, X_n\}.\]
For any finite disjoint set $X$,
\[\Big\lvert \bigcup X \Big\rvert = \sum_{A \in X} \lvert A \rvert.\]
Proof. By CARD-AR > Proposition 1.