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Lógica matemática/ ¬xyz+x¬yz+xy¬z+xyz

Expresión ¬xyz+x¬yz+xy¬z+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∧z∧(¬x))
    $$\left(x \wedge y \wedge z\right) \vee \left(x \wedge y \wedge \neg z\right) \vee \left(x \wedge z \wedge \neg y\right) \vee \left(y \wedge z \wedge \neg x\right)$$
    Solución detallada
    $$\left(x \wedge y \wedge z\right) \vee \left(x \wedge y \wedge \neg z\right) \vee \left(x \wedge z \wedge \neg y\right) \vee \left(y \wedge z \wedge \neg x\right) = \left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$
    Simplificación [src]
    $$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$ 
    (x∧y)∨(x∧z)∨(y∧z)
    Tabla de verdad 
    +---+---+---+--------+
| x | y | z | result |
+===+===+===+========+
| 0 | 0 | 0 | 0      |
+---+---+---+--------+
| 0 | 0 | 1 | 0      |
+---+---+---+--------+
| 0 | 1 | 0 | 0      |
+---+---+---+--------+
| 0 | 1 | 1 | 1      |
+---+---+---+--------+
| 1 | 0 | 0 | 0      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FNDP [src]
    $$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$ 
    (x∧y)∨(x∧z)∨(y∧z)
    FNC [src]
    $$\left(x \vee y\right) \wedge \left(x \vee z\right) \wedge \left(y \vee z\right) \wedge \left(x \vee y \vee z\right)$$ 
    (x∨y)∧(x∨z)∧(y∨z)∧(x∨y∨z)
    FND [src]
    Ya está reducido a FND
    $$\left(x \wedge y\right) \vee \left(x \wedge z\right) \vee \left(y \wedge z\right)$$ 
    (x∧y)∨(x∧z)∨(y∧z)
    FNCD [src]
    $$\left(x \vee y\right) \wedge \left(x \vee z\right) \wedge \left(y \vee z\right)$$ 
    (x∨y)∧(x∨z)∧(y∨z)
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