Sr Examen

Expresión (xy)+xz+¬x¬z

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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