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Lógica matemática/ не(a)&не(b)&cva&не(b)&не(c)va&не(b)&c

Expresión не(a)&не(b)&cva&не(b)&не(c)va&не(b)&c

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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