Expresión ¬(x*y+¬x*y*z)⇒(¬x+¬x*y+¬y)
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\left(x \wedge y\right) \vee \left(y \wedge z \wedge \neg x\right) = y \wedge \left(x \vee z\right)$$
$$\neg \left(\left(x \wedge y\right) \vee \left(y \wedge z \wedge \neg x\right)\right) = \left(\neg x \wedge \neg z\right) \vee \neg y$$
$$\left(y \wedge \neg x\right) \vee \neg x \vee \neg y = \neg x \vee \neg y$$
$$\neg \left(\left(x \wedge y\right) \vee \left(y \wedge z \wedge \neg x\right)\right) \Rightarrow \left(\left(y \wedge \neg x\right) \vee \neg x \vee \neg y\right) = 1$$
Tabla de verdad
+---+---+---+--------+
| x | y | z | result |
+===+===+===+========+
| 0 | 0 | 0 | 1 |
+---+---+---+--------+
| 0 | 0 | 1 | 1 |
+---+---+---+--------+
| 0 | 1 | 0 | 1 |
+---+---+---+--------+
| 0 | 1 | 1 | 1 |
+---+---+---+--------+
| 1 | 0 | 0 | 1 |
+---+---+---+--------+
| 1 | 0 | 1 | 1 |
+---+---+---+--------+
| 1 | 1 | 0 | 1 |
+---+---+---+--------+
| 1 | 1 | 1 | 1 |
+---+---+---+--------+