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Lógica matemática/ (¬(a*b)+(¬b*c))*(¬(a*b+¬a*¬c)+b*c)

Expresión (¬(a*b)+(¬b*c))*(¬(a*b+¬a*¬c)+b*c)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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