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Lógica matemática/ a&¬cvc&(b&¬c)v(av¬b)&c

Expresión a&¬cvc&(b&¬c)v(av¬b)&c

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    Solución

    Ha introducido [src] 
    (a∧(¬c))∨(b∧c∧(¬c))∨(c∧(a∨(¬b)))
    $$\left(a \wedge \neg c\right) \vee \left(c \wedge \left(a \vee \neg b\right)\right) \vee \left(b \wedge c \wedge \neg c\right)$$
    Solución detallada
    $$b \wedge c \wedge \neg c = \text{False}$$
    $$\left(a \wedge \neg c\right) \vee \left(c \wedge \left(a \vee \neg b\right)\right) \vee \left(b \wedge c \wedge \neg c\right) = a \vee \left(c \wedge \neg b\right)$$
    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      |
+---+---+---+--------+
    FNDP [src]
    $$a \vee \left(c \wedge \neg b\right)$$ 
    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))
    FND [src]
    Ya está reducido a FND
    $$a \vee \left(c \wedge \neg b\right)$$ 
    a∨(c∧(¬b))
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