Sr Examen

Expresión ¬((x∧y)∨(¬x∨¬z))∧((z∧¬y)∨(z∧¬x∨¬z∧x))∨((x∧y)∨(¬x∨¬z))∧¬((z∧¬y)∨(z∧¬x∨¬z∧x))

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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