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Lógica matemática/ xy∨!x(y∨xz)!(x(!y∨z)vyz)

Expresión xy∨!x(y∨xz)!(x(!y∨z)vyz)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    (x∧y)∨((¬x)∧(y∨(x∧z))∧(¬((y∧z)∨(x∧(z∨(¬y))))))
    (x∧y)∨(¬x∧¬((x∧(z∨¬y))∨(y∧z))∧(y∨(x∧z)))\left(x \wedge y\right) \vee \left(\neg x \wedge \neg \left(\left(x \wedge \left(z \vee \neg y\right)\right) \vee \left(y \wedge z\right)\right) \wedge \left(y \vee \left(x \wedge z\right)\right)\right)
    Solución detallada
    (x∧(z∨¬y))∨(y∧z)=(x∧¬y)∨(y∧z)\left(x \wedge \left(z \vee \neg y\right)\right) \vee \left(y \wedge z\right) = \left(x \wedge \neg y\right) \vee \left(y \wedge z\right)
    ¬((x∧(z∨¬y))∨(y∧z))=(y∧¬z)∨(¬x∧¬y)\neg \left(\left(x \wedge \left(z \vee \neg y\right)\right) \vee \left(y \wedge z\right)\right) = \left(y \wedge \neg z\right) \vee \left(\neg x \wedge \neg y\right)
    ¬x∧¬((x∧(z∨¬y))∨(y∧z))∧(y∨(x∧z))=y∧¬x∧¬z\neg x \wedge \neg \left(\left(x \wedge \left(z \vee \neg y\right)\right) \vee \left(y \wedge z\right)\right) \wedge \left(y \vee \left(x \wedge z\right)\right) = y \wedge \neg x \wedge \neg z
    (x∧y)∨(¬x∧¬((x∧(z∨¬y))∨(y∧z))∧(y∨(x∧z)))=y∧(x∨¬z)\left(x \wedge y\right) \vee \left(\neg x \wedge \neg \left(\left(x \wedge \left(z \vee \neg y\right)\right) \vee \left(y \wedge z\right)\right) \wedge \left(y \vee \left(x \wedge z\right)\right)\right) = y \wedge \left(x \vee \neg z\right)
    Simplificación [src]
    y∧(x∨¬z)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∧(x∨¬z)y \wedge \left(x \vee \neg z\right) 
    y∧(x∨(¬z))
    FNCD [src]
    y∧(x∨¬z)y \wedge \left(x \vee \neg z\right) 
    y∧(x∨(¬z))
    FND [src]
    (x∧y)∨(y∧¬z)\left(x \wedge y\right) \vee \left(y \wedge \neg z\right) 
    (x∧y)∨(y∧(¬z))
    FNDP [src]
    (x∧y)∨(y∧¬z)\left(x \wedge y\right) \vee \left(y \wedge \neg z\right) 
    (x∧y)∨(y∧(¬z))
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