Sr Examen

Expresión xyv¬x&(yvxz)&¬(x&(¬yvz)vyz)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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