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Lógica matemática/ xz+¬((¬y+z)(¬x+¬y))+yz

Expresión xz+¬((¬y+z)(¬x+¬y))+yz

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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