Expresión ¬(¬x3∧¬(¬x1∧x2))∨x4∧¬x5∨¬((x1∨¬x5)∧¬(¬(¬x1∨x2)∧¬x4))

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

Solución

Ha introducido [src]

(x4∧(¬x5))∨(¬((¬x3)∧(¬(x2∧(¬x1)))))∨(¬((x1∨(¬x5))∧(¬((¬x4)∧(¬(x2∨(¬x1)))))))

$$\left(x_{4} \wedge \neg x_{5}\right) \vee \neg \left(\neg x_{3} \wedge \neg \left(x_{2} \wedge \neg x_{1}\right)\right) \vee \neg \left(\neg \left(\neg x_{4} \wedge \neg \left(x_{2} \vee \neg x_{1}\right)\right) \wedge \left(x_{1} \vee \neg x_{5}\right)\right)$$

Solución detallada

$$\neg \left(x_{2} \wedge \neg x_{1}\right) = x_{1} \vee \neg x_{2}$$
$$\neg x_{3} \wedge \neg \left(x_{2} \wedge \neg x_{1}\right) = \neg x_{3} \wedge \left(x_{1} \vee \neg x_{2}\right)$$
$$\neg \left(\neg x_{3} \wedge \neg \left(x_{2} \wedge \neg x_{1}\right)\right) = x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right)$$
$$\neg \left(x_{2} \vee \neg x_{1}\right) = x_{1} \wedge \neg x_{2}$$
$$\neg x_{4} \wedge \neg \left(x_{2} \vee \neg x_{1}\right) = x_{1} \wedge \neg x_{2} \wedge \neg x_{4}$$
$$\neg \left(\neg x_{4} \wedge \neg \left(x_{2} \vee \neg x_{1}\right)\right) = x_{2} \vee x_{4} \vee \neg x_{1}$$
$$\neg \left(\neg x_{4} \wedge \neg \left(x_{2} \vee \neg x_{1}\right)\right) \wedge \left(x_{1} \vee \neg x_{5}\right) = \left(x_{1} \wedge x_{2}\right) \vee \left(x_{1} \wedge x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{5}\right)$$
$$\neg \left(\neg \left(\neg x_{4} \wedge \neg \left(x_{2} \vee \neg x_{1}\right)\right) \wedge \left(x_{1} \vee \neg x_{5}\right)\right) = \left(x_{1} \vee x_{5}\right) \wedge \left(\neg x_{1} \vee \neg x_{2}\right) \wedge \left(\neg x_{1} \vee \neg x_{4}\right)$$
$$\left(x_{4} \wedge \neg x_{5}\right) \vee \neg \left(\neg x_{3} \wedge \neg \left(x_{2} \wedge \neg x_{1}\right)\right) \vee \neg \left(\neg \left(\neg x_{4} \wedge \neg \left(x_{2} \vee \neg x_{1}\right)\right) \wedge \left(x_{1} \vee \neg x_{5}\right)\right) = x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{4} \wedge \neg x_{5}\right) \vee \left(x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right)$$

Simplificación [src]

$$x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{4} \wedge \neg x_{5}\right) \vee \left(x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right)$$

x3∨(x2∧(¬x1))∨(x4∧(¬x5))∨(x5∧(¬x1))∨(x1∧(¬x2)∧(¬x4))

Tabla de verdad

+----+----+----+----+----+--------+
| x1 | x2 | x3 | x4 | x5 | result |
+====+====+====+====+====+========+
| 0  | 0  | 0  | 0  | 0  | 0      |
+----+----+----+----+----+--------+
| 0  | 0  | 0  | 0  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 0  | 0  | 1  | 0  | 1      |
+----+----+----+----+----+--------+
| 0  | 0  | 0  | 1  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 0  | 1  | 0  | 0  | 1      |
+----+----+----+----+----+--------+
| 0  | 0  | 1  | 0  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 0  | 1  | 1  | 0  | 1      |
+----+----+----+----+----+--------+
| 0  | 0  | 1  | 1  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 0  | 0  | 0  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 0  | 0  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 0  | 1  | 0  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 0  | 1  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 1  | 0  | 0  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 1  | 0  | 1  | 1      |
+----+----+----+----+----+--------+
| 0  | 1  | 1  | 1  | 0  | 1      |
+----+----+----+----+----+--------+
| 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  | 0      |
+----+----+----+----+----+--------+
| 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  | 0      |
+----+----+----+----+----+--------+
| 1  | 1  | 0  | 0  | 1  | 0      |
+----+----+----+----+----+--------+
| 1  | 1  | 0  | 1  | 0  | 1      |
+----+----+----+----+----+--------+
| 1  | 1  | 0  | 1  | 1  | 0      |
+----+----+----+----+----+--------+
| 1  | 1  | 1  | 0  | 0  | 1      |
+----+----+----+----+----+--------+
| 1  | 1  | 1  | 0  | 1  | 1      |
+----+----+----+----+----+--------+
| 1  | 1  | 1  | 1  | 0  | 1      |
+----+----+----+----+----+--------+
| 1  | 1  | 1  | 1  | 1  | 1      |
+----+----+----+----+----+--------+

FNC [src]

$$\left(x_{1} \vee x_{3} \vee x_{4} \vee \neg x_{1}\right) \wedge \left(x_{1} \vee x_{3} \vee \neg x_{1} \vee \neg x_{5}\right) \wedge \left(x_{3} \vee x_{4} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{3} \vee x_{4} \vee \neg x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{4} \vee \neg x_{5}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{3} \vee x_{4} \vee x_{5}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{3} \vee x_{4} \vee \neg x_{1}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{3} \vee x_{5} \vee \neg x_{5}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{3} \vee \neg x_{1} \vee \neg x_{5}\right) \wedge \left(x_{1} \vee x_{3} \vee x_{4} \vee x_{5} \vee \neg x_{1}\right) \wedge \left(x_{1} \vee x_{3} \vee x_{5} \vee \neg x_{1} \vee \neg x_{5}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{4} \vee x_{5} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{4} \vee x_{5} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{4} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{4} \vee \neg x_{1} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{5} \vee \neg x_{2} \vee \neg x_{5}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{5} \vee \neg x_{4} \vee \neg x_{5}\right) \wedge \left(x_{2} \vee x_{3} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}\right) \wedge \left(x_{2} \vee x_{3} \vee \neg x_{1} \vee \neg x_{4} \vee \neg x_{5}\right) \wedge \left(x_{3} \vee x_{4} \vee x_{5} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{3} \vee x_{4} \vee x_{5} \vee \neg x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee x_{5} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}\right) \wedge \left(x_{3} \vee x_{5} \vee \neg x_{1} \vee \neg x_{4} \vee \neg x_{5}\right)$$

(x1∨x3∨x4∨(¬x1))∧(x1∨x2∨x3∨x4∨x5)∧(x1∨x3∨(¬x1)∨(¬x5))∧(x3∨x4∨(¬x1)∨(¬x2))∧(x3∨x4∨(¬x1)∨(¬x4))∧(x1∨x2∨x3∨x4∨(¬x1))∧(x1∨x2∨x3∨x5∨(¬x5))∧(x1∨x3∨x4∨x5∨(¬x1))∧(x2∨x3∨x4∨x5∨(¬x2))∧(x2∨x3∨x4∨x5∨(¬x4))∧(x3∨(¬x1)∨(¬x2)∨(¬x5))∧(x3∨(¬x1)∨(¬x4)∨(¬x5))∧(x1∨x2∨x3∨(¬x1)∨(¬x5))∧(x1∨x3∨x5∨(¬x1)∨(¬x5))∧(x2∨x3∨x4∨(¬x1)∨(¬x2))∧(x2∨x3∨x4∨(¬x1)∨(¬x4))∧(x2∨x3∨x5∨(¬x2)∨(¬x5))∧(x2∨x3∨x5∨(¬x4)∨(¬x5))∧(x3∨x4∨x5∨(¬x1)∨(¬x2))∧(x3∨x4∨x5∨(¬x1)∨(¬x4))∧(x2∨x3∨(¬x1)∨(¬x2)∨(¬x5))∧(x2∨x3∨(¬x1)∨(¬x4)∨(¬x5))∧(x3∨x5∨(¬x1)∨(¬x2)∨(¬x5))∧(x3∨x5∨(¬x1)∨(¬x4)∨(¬x5))

FNDP [src]

$$x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{4} \wedge \neg x_{5}\right) \vee \left(x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right)$$

x3∨(x2∧(¬x1))∨(x4∧(¬x5))∨(x5∧(¬x1))∨(x1∧(¬x2)∧(¬x4))

FNCD [src]

$$\left(x_{3} \vee x_{4} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{4} \vee \neg x_{5}\right) \wedge \left(x_{1} \vee x_{2} \vee x_{3} \vee x_{4} \vee x_{5}\right)$$

(x1∨x2∨x3∨x4∨x5)∧(x3∨x4∨(¬x1)∨(¬x2))∧(x3∨(¬x1)∨(¬x4)∨(¬x5))

FND [src]

Ya está reducido a FND

$$x_{3} \vee \left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{4} \wedge \neg x_{5}\right) \vee \left(x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right)$$

x3∨(x2∧(¬x1))∨(x4∧(¬x5))∨(x5∧(¬x1))∨(x1∧(¬x2)∧(¬x4))

¿Cómo usar?

Expresiones idénticas

Expresión ¬(¬x3∧¬(¬x1∧x2))∨x4∧¬x5∨¬((x1∨¬x5)∧¬(¬(¬x1∨x2)∧¬x4))

Solución