Sr Examen

Expresión x*y*z˅¬x*y*z˅x¬y*z

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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