Sr Examen

Expresión abd+a¬bcd+¬abcd+¬ab¬c+¬ac¬d+abc¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

    Solución

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