$$$\left(X \cdot Y\right) + \overline{Y \cdot Z} + \left(X \cdot \overline{Y} \cdot Z \cdot \left(\left(X \cdot Y\right) + Z\right)\right)$$$을(를) 간단히 하세요

교환법칙을 적용하세요:

$$\left(X \cdot Y\right) + \overline{Y \cdot Z} + \left(X \cdot \overline{Y} \cdot Z \cdot {\color{red}\left(\left(X \cdot Y\right) + Z\right)}\right) = \left(X \cdot Y\right) + \overline{Y \cdot Z} + \left(X \cdot \overline{Y} \cdot Z \cdot {\color{red}\left(Z + \left(X \cdot Y\right)\right)}\right)$$

흡수 법칙 $$$x \cdot \left(x + y\right) = x$$$을 $$$x = Z$$$ 및 $$$y = X \cdot Y$$$에 적용하십시오:

$$\left(X \cdot Y\right) + \overline{Y \cdot Z} + \left(X \cdot \overline{Y} \cdot {\color{red}\left(Z \cdot \left(Z + \left(X \cdot Y\right)\right)\right)}\right) = \left(X \cdot Y\right) + \overline{Y \cdot Z} + \left(X \cdot \overline{Y} \cdot {\color{red}\left(Z\right)}\right)$$

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

$$\left(X \cdot Y\right) + {\color{red}\left(\overline{Y \cdot Z}\right)} + \left(X \cdot \overline{Y} \cdot Z\right) = \left(X \cdot Y\right) + {\color{red}\left(\overline{Y} + \overline{Z}\right)} + \left(X \cdot \overline{Y} \cdot Z\right)$$

교환법칙을 적용하세요:

$${\color{red}\left(\left(X \cdot Y\right) + \overline{Y} + \overline{Z} + \left(X \cdot \overline{Y} \cdot Z\right)\right)} = {\color{red}\left(\left(X \cdot Y\right) + \overline{Y} + \left(X \cdot \overline{Y} \cdot Z\right) + \overline{Z}\right)}$$

교환법칙을 적용하세요:

$$\left(X \cdot Y\right) + \overline{Y} + {\color{red}\left(X \cdot \overline{Y} \cdot Z\right)} + \overline{Z} = \left(X \cdot Y\right) + \overline{Y} + {\color{red}\left(\overline{Y} \cdot X \cdot Z\right)} + \overline{Z}$$

흡수 법칙 $$$x + \left(x \cdot y\right) = x$$$을 $$$x = \overline{Y}$$$ 및 $$$y = X \cdot Z$$$에 적용하십시오:

$$\left(X \cdot Y\right) + {\color{red}\left(\overline{Y} + \left(\overline{Y} \cdot X \cdot Z\right)\right)} + \overline{Z} = \left(X \cdot Y\right) + {\color{red}\left(\overline{Y}\right)} + \overline{Z}$$

교환법칙을 적용하세요:

$${\color{red}\left(\left(X \cdot Y\right) + \overline{Y} + \overline{Z}\right)} = {\color{red}\left(\overline{Y} + \left(X \cdot Y\right) + \overline{Z}\right)}$$

교환법칙을 적용하세요:

$$\overline{Y} + {\color{red}\left(X \cdot Y\right)} + \overline{Z} = \overline{Y} + {\color{red}\left(Y \cdot X\right)} + \overline{Z}$$

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

$${\color{red}\left(\overline{Y} + \left(Y \cdot X\right)\right)} + \overline{Z} = {\color{red}\left(\overline{Y} + X\right)} + \overline{Z}$$