Sr Examen
Lógica matemática/ (a∨b)∧(a∨c)∧(a∨d)∧(b∨e)∧(c∨d)∧(c∨e)∧(d∨e)∧(a∨(¬e))∧(c∨(¬b))∧(d∨(¬b))∧(e∨(¬a))∧((¬a)∨(¬b))∧((¬b)∨(¬e))∧(b∨(¬c)∨(¬d))∧((¬a)∨(¬c)∨(¬d))∧((¬c)∨(¬¬((a∨b)∧(a∨c))d)∨(¬e))

Expresión (a∨b)∧(a∨c)∧(a∨d)∧(b∨e)∧(c∨d)∧(c∨e)∧(d∨e)∧(a∨(¬e))∧(c∨(¬b))∧(d∨(¬b))∧(e∨(¬a))∧((¬a)∨(¬b))∧((¬b)∨(¬e))∧(b∨(¬c)∨(¬d))∧((¬a)∨(¬c)∨(¬d))∧((¬c)∨(¬¬((a∨b)∧(a∨c))d)∨(¬e))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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