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Lógica matemática/ ¬(a∧b∨b∧c)∨c∧¬a

Expresión ¬(a∧b∨b∧c)∨c∧¬a

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    Solución

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