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Lógica matemática/ ABC+(((¬(¬A¬C))¬B)A)

Expresión ABC+(((¬(¬A¬C))¬B)A)

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    Solución

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