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Lógica matemática/ AB¬CD+¬ACD+¬BC

Expresión AB¬CD+¬ACD+¬BC

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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