Sr Examen

Expresión xy¬z∨¬xy¬z∨x¬y

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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