Sr Examen

Expresión ¬(x*y+¬x*y*z)⇒(¬x+¬(x*y+¬y))

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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