定理 De Morgan 定律

给定非空集合 $X$ 和其子集 $A,B \subset X$
则成立

$$ \bbox[5pt]{ \begin{aligned} X \backslash (A \cap B) = (X \backslash A) \cup (X \backslash B) \\ X \backslash (A \cup B) = (X \backslash A) \cap (X \backslash B) \end{aligned} } $$

证明