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Lógica matemática/ xy∨¬(x(y∨z)∨yz)

Expresión xy∨¬(x(y∨z)∨yz)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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