化简 $$$0 \oplus 1$$$

将公式 $$$x \oplus y = \left(x \cdot \overline{y}\right) + \left(\overline{x} \cdot y\right)$$$ 应用于 $$$x = 0$$$ 和 $$$y = 1$$$：

$${\color{red}\left(0 \oplus 1\right)} = {\color{red}\left(\left(0 \cdot \overline{1}\right) + \left(\overline{0} \cdot 1\right)\right)}$$

应用否定律 $$$\overline{1} = 0$$$：

$$\left(0 \cdot {\color{red}\left(\overline{1}\right)}\right) + \left(\overline{0} \cdot 1\right) = \left(0 \cdot {\color{red}\left(0\right)}\right) + \left(\overline{0} \cdot 1\right)$$

应用否定律 $$$\overline{0} = 1$$$：

$$\left(0 \cdot 0\right) + \left({\color{red}\left(\overline{0}\right)} \cdot 1\right) = \left(0 \cdot 0\right) + \left({\color{red}\left(1\right)} \cdot 1\right)$$

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

$${\color{red}\left(0 \cdot 0\right)} + \left(1 \cdot 1\right) = {\color{red}\left(0\right)} + \left(1 \cdot 1\right)$$

应用交换律：

$${\color{red}\left(0 + \left(1 \cdot 1\right)\right)} = {\color{red}\left(\left(1 \cdot 1\right) + 0\right)}$$

对 $$$x = 1 \cdot 1$$$ 应用恒等律 $$$x + 0 = x$$$：

$${\color{red}\left(\left(1 \cdot 1\right) + 0\right)} = {\color{red}\left(1 \cdot 1\right)}$$

对 $$$x = 1$$$ 应用恒等律 $$$x \cdot 1 = x$$$：

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