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Lógica matemática/ !(!(a&b)&cva&b&(!c)va&c)

Expresión !(!(a&b)&cva&b&(!c)va&c)

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    Solución

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