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Lógica matemática/ ¬a&cva&¬bvb&¬c(¬avb&c)

Expresión ¬a&cva&¬bvb&¬c(¬avb&c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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