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Lógica matemática/ Cv¬(BvA&C)&A

Expresión Cv¬(BvA&C)&A

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    Solución

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