Sr Examen

Expresión (xvy)y(xvyvy)⇔(((xy)⊕¬(xvy))v(xy))

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

    Ha introducido [src]
    (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
    $$y \wedge \left(x \vee y\right) = y$$
    $$\neg \left(x \vee y\right) = \neg x \wedge \neg y$$
    $$\left(x \wedge y\right) ⊕ \neg \left(x \vee y\right) = \left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right)$$
    $$\left(x \wedge y\right) \vee \left(\left(x \wedge y\right) ⊕ \neg \left(x \vee y\right)\right) = \left(x \wedge y\right) \vee \left(\neg x \wedge \neg y\right)$$
    $$\left(y \wedge \left(x \vee y\right)\right) ⇔ \left(\left(x \wedge y\right) \vee \left(\left(x \wedge y\right) ⊕ \neg \left(x \vee y\right)\right)\right) = x$$
    Simplificación [src]
    $$x$$
    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
    $$x$$
    x
    FND [src]
    Ya está reducido a FND
    $$x$$
    x
    FNDP [src]
    $$x$$
    x
    FNCD [src]
    $$x$$
    x