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Lógica matemática/ ¬(¬xvy)*v*(z≡y)*vw

Expresión ¬(¬xvy)*v*(z≡y)*vw

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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