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Lógica matemática/ -a*(-b*c+b*-c)

Expresión -a*(-b*c+b*-c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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