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Lógica matemática/ ABC+AB¬C+¬A¬BC

Expresión ABC+AB¬C+¬A¬BC

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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