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Lógica matemática/ ¬(¬(xy)&(x¬yzv¬xy))

Expresión ¬(¬(xy)&(x¬yzv¬xy))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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