Sr Examen
Lógica matemática/ (B∨A∧C∨¬A∧¬C)∧(¬A∨B∧C∨¬B∧¬C)∧(¬A∨¬B∨¬C)

Expresión (B∨A∧C∨¬A∧¬C)∧(¬A∨B∧C∨¬B∧¬C)∧(¬A∨¬B∨¬C)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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