Sr Examen

Expresión ((avc)&(avd))&((cv(c&b)&c)va)

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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