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Lógica matemática/ ab¬c¬dva¬b¬c¬dvab¬cdv¬ab¬c¬dv¬a¬b¬c¬d

Expresión ab¬c¬dva¬b¬c¬dvab¬cdv¬ab¬c¬dv¬a¬b¬c¬d

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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