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