Sr Examen
Lógica matemática/ (avbvc)&¬(¬a&b&¬c)&(avbv¬(c&d))&¬(¬avbvcvdve)va&(¬bv¬c)v(¬avb&c)&(avd&e)

Expresión (avbvc)&¬(¬a&b&¬c)&(avbv¬(c&d))&¬(¬avbvcvdve)va&(¬bv¬c)v(¬avb&c)&(avd&e)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

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