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Lógica matemática/ с&(¬сvb)&(av¬b)v¬b

Expresión с&(¬сvb)&(av¬b)v¬b

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    Solución

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