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Lógica matemática/ ¬(¬A∧¬B∧¬C∧¬D+¬A∧¬B∧C∧D+¬A∧B∧C∧¬D)

Expresión ¬(¬A∧¬B∧¬C∧¬D+¬A∧¬B∧C∧D+¬A∧B∧C∧¬D)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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