化简 $$$\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}$$$

应用交换律：

$${\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A \cdot \overline{B}\right)} = {\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A\right)}$$

将幂等律 $$$x \cdot x = x$$$ 应用于 $$$x = \overline{B}$$$：

$$\overline{A} \cdot {\color{red}\left(\overline{B} \cdot \overline{B}\right)} \cdot \overline{C} \cdot \overline{D} \cdot A = \overline{A} \cdot {\color{red}\left(\overline{B}\right)} \cdot \overline{C} \cdot \overline{D} \cdot A$$

应用交换律：

$${\color{red}\left(\overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} \cdot A\right)} = {\color{red}\left(A \cdot \overline{A} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}\right)}$$

对 $$$x = A$$$ 应用补集律 $$$x \cdot \overline{x} = 0$$$：

$${\color{red}\left(A \cdot \overline{A}\right)} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}$$

应用交换律：

$${\color{red}\left(0 \cdot \overline{B} \cdot \overline{C} \cdot \overline{D}\right)} = {\color{red}\left(\overline{B} \cdot 0 \cdot \overline{C} \cdot \overline{D}\right)}$$

对 $$$x = \overline{B}$$$ 应用支配（零化、湮灭）律 $$$x \cdot 0 = 0$$$：

$${\color{red}\left(\overline{B} \cdot 0\right)} \cdot \overline{C} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{C} \cdot \overline{D}$$

应用交换律：

$${\color{red}\left(0 \cdot \overline{C} \cdot \overline{D}\right)} = {\color{red}\left(\overline{C} \cdot 0 \cdot \overline{D}\right)}$$

对 $$$x = \overline{C}$$$ 应用支配（零化、湮灭）律 $$$x \cdot 0 = 0$$$：

$${\color{red}\left(\overline{C} \cdot 0\right)} \cdot \overline{D} = {\color{red}\left(0\right)} \cdot \overline{D}$$

应用交换律：

$${\color{red}\left(0 \cdot \overline{D}\right)} = {\color{red}\left(\overline{D} \cdot 0\right)}$$

对 $$$x = \overline{D}$$$ 应用支配（零化、湮灭）律 $$$x \cdot 0 = 0$$$：

$${\color{red}\left(\overline{D} \cdot 0\right)} = {\color{red}\left(0\right)}$$