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Lógica matemática/ ¬((¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C))))

Expresión ¬((¬((A∨B)∧C))∨¬(¬((a∧b)∨(b∧C))))

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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