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

Expresión ¬((¬(a∨b)∧c)∨(¬(a∧b∨b∧c)))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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