下面介绍几种集合的运算律:

(1) 交换律

$\begin{align}& A\cap B=B\cap A, \\& A\cup B=B\cup A \\ \end{align}$

(2) 结合律

$\begin{align} & A\cap (B\cap C)=(\text{A}\cap \text{B})\cap \text{C} \\ & \text{A}\cup (B\cup C)=(A\cup B)\cup C \\ \end{align}$

(3) 分配律

$\begin{align}& A\cap (B\cup C)=(\text{A}\cap \text{B})\cup (\text{A}\cap \text{C}) \\ & \text{A}\cup (B\cap C)=(A\cup B)\cap (A\cup C) \\ \end{align}$
（4）笛·摩根定理

$\begin{align}& \complement \text{u}(A\cap B)=(\complement \text{u}A)\cup (\complement \text{u}B), \\ & \complement \text{u}(A\cup B)=(\complement \text{u}A)\cap (\complement \text{u}B) \\ \end{align}$