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Lógica matemática/ ¬a^b(bvc)va^¬b

Expresión ¬a^b(bvc)va^¬b

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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