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

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