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Lógica matemática/ av¬b&cv¬(a⇒¬(¬b&c))

Expresión av¬b&cv¬(a⇒¬(¬b&c))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

    Ha introducido [src] 
    a∨(c∧(¬b))∨(¬(a⇒(¬(c∧(¬b)))))
    $$a \vee \left(c \wedge \neg b\right) \vee a \not\Rightarrow \neg \left(c \wedge \neg b\right)$$
    Solución detallada
    $$\neg \left(c \wedge \neg b\right) = b \vee \neg c$$
    $$a \Rightarrow \neg \left(c \wedge \neg b\right) = b \vee \neg a \vee \neg c$$
    $$a \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \wedge c \wedge \neg b$$
    $$a \vee \left(c \wedge \neg b\right) \vee a \not\Rightarrow \neg \left(c \wedge \neg b\right) = a \vee \left(c \wedge \neg b\right)$$
    Simplificación [src]
    $$a \vee \left(c \wedge \neg b\right)$$ 
    a∨(c∧(¬b))
    Tabla de verdad 
    +---+---+---+--------+
| a | b | c | result |
+===+===+===+========+
| 0 | 0 | 0 | 0      |
+---+---+---+--------+
| 0 | 0 | 1 | 1      |
+---+---+---+--------+
| 0 | 1 | 0 | 0      |
+---+---+---+--------+
| 0 | 1 | 1 | 0      |
+---+---+---+--------+
| 1 | 0 | 0 | 1      |
+---+---+---+--------+
| 1 | 0 | 1 | 1      |
+---+---+---+--------+
| 1 | 1 | 0 | 1      |
+---+---+---+--------+
| 1 | 1 | 1 | 1      |
+---+---+---+--------+
    FND [src]
    Ya está reducido a FND
    $$a \vee \left(c \wedge \neg b\right)$$ 
    a∨(c∧(¬b))
    FNC [src]
    $$\left(a \vee c\right) \wedge \left(a \vee \neg b\right)$$ 
    (a∨c)∧(a∨(¬b))
    FNCD [src]
    $$\left(a \vee c\right) \wedge \left(a \vee \neg b\right)$$ 
    (a∨c)∧(a∨(¬b))
    FNDP [src]
    $$a \vee \left(c \wedge \neg b\right)$$ 
    a∨(c∧(¬b))
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