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Lógica matemática/ (a∨b∨c)∧(¬a∨b∨c)∧(¬a∨b∨¬c)∧(¬a∨¬b∨¬c)

Expresión (a∨b∨c)∧(¬a∨b∨c)∧(¬a∨b∨¬c)∧(¬a∨¬b∨¬c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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