Expresión ¬((x∧y)∨(¬x∨¬z))∧((z∧¬y)∨(z∧¬x∨¬z∧x))∨((x∧y)∨(¬x∨¬z))∧¬((z∧¬y)∨(z∧¬x∨¬z∧x))
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
$$\left(x \wedge y\right) \vee \neg x \vee \neg z = y \vee \neg x \vee \neg z$$
$$\neg \left(\left(x \wedge y\right) \vee \neg x \vee \neg z\right) = x \wedge z \wedge \neg y$$
$$\neg \left(\left(x \wedge y\right) \vee \neg x \vee \neg z\right) \wedge \left(\left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(z \wedge \neg y\right)\right) = x \wedge z \wedge \neg y$$
$$\neg \left(\left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(z \wedge \neg y\right)\right) = \left(x \vee \neg z\right) \wedge \left(y \vee \neg z\right) \wedge \left(z \vee \neg x\right)$$
$$\neg \left(\left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(z \wedge \neg y\right)\right) \wedge \left(\left(x \wedge y\right) \vee \neg x \vee \neg z\right) = \left(x \vee \neg z\right) \wedge \left(y \vee \neg x\right) \wedge \left(z \vee \neg x\right)$$
$$\left(\neg \left(\left(x \wedge y\right) \vee \neg x \vee \neg z\right) \wedge \left(\left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(z \wedge \neg y\right)\right)\right) \vee \left(\neg \left(\left(x \wedge \neg z\right) \vee \left(z \wedge \neg x\right) \vee \left(z \wedge \neg y\right)\right) \wedge \left(\left(x \wedge y\right) \vee \neg x \vee \neg z\right)\right) = \left(x \wedge z\right) \vee \left(\neg x \wedge \neg z\right)$$
$$\left(x \wedge z\right) \vee \left(\neg x \wedge \neg z\right)$$
Tabla de verdad
+---+---+---+--------+
| x | y | z | result |
+===+===+===+========+
| 0 | 0 | 0 | 1 |
+---+---+---+--------+
| 0 | 0 | 1 | 0 |
+---+---+---+--------+
| 0 | 1 | 0 | 1 |
+---+---+---+--------+
| 0 | 1 | 1 | 0 |
+---+---+---+--------+
| 1 | 0 | 0 | 0 |
+---+---+---+--------+
| 1 | 0 | 1 | 1 |
+---+---+---+--------+
| 1 | 1 | 0 | 0 |
+---+---+---+--------+
| 1 | 1 | 1 | 1 |
+---+---+---+--------+
$$\left(x \wedge z\right) \vee \left(\neg x \wedge \neg z\right)$$
$$\left(x \vee \neg x\right) \wedge \left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right) \wedge \left(z \vee \neg z\right)$$
(x∨(¬x))∧(x∨(¬z))∧(z∨(¬x))∧(z∨(¬z))
Ya está reducido a FND
$$\left(x \wedge z\right) \vee \left(\neg x \wedge \neg z\right)$$
$$\left(x \vee \neg z\right) \wedge \left(z \vee \neg x\right)$$