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Lógica matemática/ yv(x⇔z)

Expresión yv(x⇔z)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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