Sr Examen

Expresión ¬(x2&x1⊕x3+¬x1⊕x3&x1)⊕(x2+¬x1)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

    Ha introducido [src]
    (x2∨(¬x1))⊕(¬((x1∧x2)⊕(x1∧x3)⊕(x3∨(¬x1))))
    $$\left(x_{2} \vee \neg x_{1}\right) ⊕ \neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right)$$
    Solución detallada
    $$\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right) = x_{2} \vee \neg x_{1}$$
    $$\neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right) = x_{1} \wedge \neg x_{2}$$
    $$\left(x_{2} \vee \neg x_{1}\right) ⊕ \neg \left(\left(x_{1} \wedge x_{2}\right) ⊕ \left(x_{1} \wedge x_{3}\right) ⊕ \left(x_{3} \vee \neg x_{1}\right)\right) = 1$$
    Simplificación [src]
    1
    1
    Tabla de verdad
    +----+----+----+--------+
    | x1 | x2 | x3 | result |
    +====+====+====+========+
    | 0  | 0  | 0  | 1      |
    +----+----+----+--------+
    | 0  | 0  | 1  | 1      |
    +----+----+----+--------+
    | 0  | 1  | 0  | 1      |
    +----+----+----+--------+
    | 0  | 1  | 1  | 1      |
    +----+----+----+--------+
    | 1  | 0  | 0  | 1      |
    +----+----+----+--------+
    | 1  | 0  | 1  | 1      |
    +----+----+----+--------+
    | 1  | 1  | 0  | 1      |
    +----+----+----+--------+
    | 1  | 1  | 1  | 1      |
    +----+----+----+--------+
    FNDP [src]
    1
    1
    FND [src]
    Ya está reducido a FND
    1
    1
    FNC [src]
    Ya está reducido a FNC
    1
    1
    FNCD [src]
    1
    1