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Lógica matemática/ z˄(x˄y̅˅x)˄z̅˄x̅˅y

Expresión z˄(x˄y̅˅x)˄z̅˄x̅˅y

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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