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Lógica matemática/ (¬a∨¬(abc)∨¬c)(a¬c∨c¬x∨x)¬(ac∨bx)

Expresión (¬a∨¬(abc)∨¬c)(a¬c∨c¬x∨x)¬(ac∨bx)

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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