Sr Examen
Lógica matemática/ (avbvc)(avbv!c)(!avbvc)(!av!bvc)(!av!bv!c)

Expresión (avbvc)(avbv!c)(!avbvc)(!av!bvc)(!av!bv!c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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