$$$\overline{\left(\overline{A} + B\right) \cdot \left(\overline{B} + C\right)}$$$을(를) 간단히 하세요

$$$x = \overline{A} + B$$$와 $$$y = \overline{B} + C$$$에 대해 드모르간의 법칙 $$$\overline{x \cdot y} = \overline{x} + \overline{y}$$$ 적용:

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

$$$x = \overline{A}$$$와 $$$y = B$$$에 대해 드모르간의 법칙 $$$\overline{x + y} = \overline{x} \cdot \overline{y}$$$ 적용:

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

$$$x = A$$$에 대해 이중 부정(involution) 법칙 $$$\overline{\overline{x}} = x$$$을 적용하십시오:

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

$$$x = \overline{B}$$$와 $$$y = C$$$에 대해 드모르간의 법칙 $$$\overline{x + y} = \overline{x} \cdot \overline{y}$$$ 적용:

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

$$$x = B$$$에 대해 이중 부정(involution) 법칙 $$$\overline{\overline{x}} = x$$$을 적용하십시오:

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