Sr Examen
Lógica matemática/ ¬((¬a+c+¬d+e+¬g)*(b+c+¬d+e+¬g))+(b+c)*¬a+(d+g)*¬(d*¬e)+(¬(¬c*d)+g*e)*¬(a*¬d*g)*(b+g)

Expresión ¬((¬a+c+¬d+e+¬g)*(b+c+¬d+e+¬g))+(b+c)*¬a+(d+g)*¬(d*¬e)+(¬(¬c*d)+g*e)*¬(a*¬d*g)*(b+g)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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