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Lógica matemática/ ABCvAB¬CvA¬BC¬ABCv¬AB¬C

Expresión ABCvAB¬CvA¬BC¬ABCv¬AB¬C

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    Solución

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