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Lógica matemática/ AC¬B∨ACD∨B¬AD∨BCD

Expresión AC¬B∨ACD∨B¬AD∨BCD

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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