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Lógica matemática/ xyzvx¬zyv¬xy¬zvxy¬zvxyz

Expresión xyzvx¬zyv¬xy¬zvxy¬zvxyz

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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