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Lógica matemática/ (b&cva&(!b)&(!c)v(!a)&c)&(a&bv(!c)va&c)

Expresión (b&cva&(!b)&(!c)v(!a)&c)&(a&bv(!c)va&c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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