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

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

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

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

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

다시 쓰기:

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

교환법칙을 적용하세요:

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

변수 $$$x = \overline{B}$$$와 $$$y = \overline{C}$$$에 대해 중복 법칙 $$$x + \left(\overline{x} \cdot y\right) = x + y$$$을(를) 적용하십시오:

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

다시 쓰기:

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

교환법칙을 적용하세요:

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

$$$x = C$$$에 대해 여사건 법칙 $$$x + \overline{x} = 1$$$를 적용하세요:

$$\left({\color{red}\left(C + \overline{C}\right)} + \overline{B}\right) \cdot \overline{A} = \left({\color{red}\left(1\right)} + \overline{B}\right) \cdot \overline{A}$$

교환법칙을 적용하세요:

$${\color{red}\left(1 + \overline{B}\right)} \cdot \overline{A} = {\color{red}\left(\overline{B} + 1\right)} \cdot \overline{A}$$

$$$x = \overline{B}$$$에 대해 지배(영, 무효) 법칙 $$$x + 1 = 1$$$을 적용하세요:

$${\color{red}\left(\overline{B} + 1\right)} \cdot \overline{A} = {\color{red}\left(1\right)} \cdot \overline{A}$$

교환법칙을 적용하세요:

$${\color{red}\left(1 \cdot \overline{A}\right)} = {\color{red}\left(\overline{A} \cdot 1\right)}$$

항등법칙 $$$x \cdot 1 = x$$$을 $$$x = \overline{A}$$$에 적용하십시오:

$${\color{red}\left(\overline{A} \cdot 1\right)} = {\color{red}\left(\overline{A}\right)}$$