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Lógica matemática/ ¬((¬avb)&c)v¬(avbvc)

Expresión ¬((¬avb)&c)v¬(avbvc)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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