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Lógica matemática/ y(xvy)⇔(((xy)⊕¬(xvy))vxy)

Expresión y(xvy)⇔(((xy)⊕¬(xvy))vxy)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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