Sr Examen

Expresión cdv¬c¬bv¬db

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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