Sr Examen

Expresión ¬(x¬yv¬xz)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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