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Lógica matemática/ bc+a(¬bc+b¬c)

Expresión bc+a(¬bc+b¬c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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