Sr Examen

Expresión ((xy⊕(xvy))vy)((y⊕(xvy))vyxy)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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