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Lógica matemática/ y&((x≡y)∨z)

Expresión y&((x≡y)∨z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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