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Lógica matemática/ avb&¬av¬b&¬¬avc&a

Expresión avb&¬av¬b&¬¬avc&a

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    Solución

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