Sr Examen
Lógica matemática/ c&(!av!c)va&b&!c

Expresión c&(!av!c)va&b&!c

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    Solución

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