Teorema del consenso(algebra di Boole)

Related

• Algebra Booleana
• Progettazione Sistemi Digitali (class)

Teorema

$$\begin{array}{rl}& -xy+\overline{x}z+yz=xy+\overline{x}z\\ & \\ & -(x+y)\cdot (\overline{x}+z)\cdot (y+z)=(x+y)\cdot (\overline{x}z)\end{array}$$

Dimostrazione

$$\begin{array}{rl}xy+\bar{x}z+yz& =xy+\bar{x}z+yz(x+\bar{x})\\ & =xy+\bar{x}z+xyz+\bar{x}yz\\ & =xy+xyz+\bar{x}z+\bar{x}yz\\ & =xy(1+z)+\bar{x}z(1+y)\\ & =xy(1)+\bar{x}z(1)\\ & =xy+\bar{x}z\end{array}$$