Sr Examen
Lógica matemática/ a&-b&сvc&-b&-ava&b&c

Expresión a&-b&сvc&-b&-ava&b&c

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    Solución

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