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Lógica matemática/ z*(x+y)+x*y*z*(y+z)

Expresión z*(x+y)+x*y*z*(y+z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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