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Lógica matemática/ x*y∨¬(x*(y∨z)∨y*z)

Expresión x*y∨¬(x*(y∨z)∨y*z)

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))))
    (x∧y)∨¬((x∧(y∨z))∨(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
    (x∧(y∨z))∨(y∧z)=(x∧y)∨(x∧z)∨(y∧z)\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)
    ¬((x∧(y∨z))∨(y∧z))=(¬x∧¬y)∨(¬x∧¬z)∨(¬y∧¬z)\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)
    (x∧y)∨¬((x∧(y∨z))∨(y∧z))=(x∧y)∨(¬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) = \left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right) \vee \neg z
    Simplificación [src]
    (x∧y)∨(¬x∧¬y)∨¬z\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      |
+---+---+---+--------+
    FNDP [src]
    (x∧y)∨(¬x∧¬y)∨¬z\left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right) \vee \neg z 
    (¬z)∨(x∧y)∨((¬x)∧(¬y))
    FNC [src]
    (x∨¬x∨¬z)∧(x∨¬y∨¬z)∧(y∨¬x∨¬z)∧(y∨¬y∨¬z)\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
    (x∧y)∨(¬x∧¬y)∨¬z\left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right) \vee \neg z 
    (¬z)∨(x∧y)∨((¬x)∧(¬y))
    FNCD [src]
    (x∨¬y∨¬z)∧(y∨¬x∨¬z)\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))
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