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Lógica matemática/ А(a∨ab¬c)∨¬a¬b¬c

Expresión А(a∨ab¬c)∨¬a¬b¬c

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    Solución

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