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Lógica matemática/ a∧(¬(¬c∧¬b))∨(¬(¬a∨b))∧c∨a∧c

Expresión a∧(¬(¬c∧¬b))∨(¬(¬a∨b))∧c∨a∧c

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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