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Lógica matemática/ (xyz)v(x(¬y)z)v((¬x)y(¬z))v(xy(¬z))v(xyz)

Expresión (xyz)v(x(¬y)z)v((¬x)y(¬z))v(xy(¬z))v(xyz)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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