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

Expresión ¬((¬a)*b∨a*(b∨(¬c)))

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    Solución

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