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Lógica matemática/ xv(z∧¬w)v(y∧¬w)v(y∧¬z)

Expresión xv(z∧¬w)v(y∧¬w)v(y∧¬z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    x∨(y∧(¬w))∨(y∧(¬z))∨(z∧(¬w))
    $$x \vee \left(y \wedge \neg w\right) \vee \left(y \wedge \neg z\right) \vee \left(z \wedge \neg w\right)$$
    Solución detallada
    $$x \vee \left(y \wedge \neg w\right) \vee \left(y \wedge \neg z\right) \vee \left(z \wedge \neg w\right) = x \vee \left(y \wedge \neg z\right) \vee \left(z \wedge \neg w\right)$$
    Simplificación [src]
    $$x \vee \left(y \wedge \neg z\right) \vee \left(z \wedge \neg w\right)$$ 
    x∨(y∧(¬z))∨(z∧(¬w))
    Tabla de verdad 
    +---+---+---+---+--------+
| w | x | y | z | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 0      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNC [src]
    $$\left(x \vee y \vee z\right) \wedge \left(x \vee y \vee \neg w\right) \wedge \left(x \vee z \vee \neg z\right) \wedge \left(x \vee \neg w \vee \neg z\right)$$ 
    (x∨y∨z)∧(x∨y∨(¬w))∧(x∨z∨(¬z))∧(x∨(¬w)∨(¬z))
    FND [src]
    Ya está reducido a FND
    $$x \vee \left(y \wedge \neg z\right) \vee \left(z \wedge \neg w\right)$$ 
    x∨(y∧(¬z))∨(z∧(¬w))
    FNDP [src]
    $$x \vee \left(y \wedge \neg z\right) \vee \left(z \wedge \neg w\right)$$ 
    x∨(y∧(¬z))∨(z∧(¬w))
    FNCD [src]
    $$\left(x \vee y \vee z\right) \wedge \left(x \vee \neg w \vee \neg z\right)$$ 
    (x∨y∨z)∧(x∨(¬w)∨(¬z))
    © Sr Examen