Expresión ¬(¬(¬X1∧X2)∧¬X3∨¬(X2∨¬X4))∨¬X4

Ha introducido [src]

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

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

Solución detallada

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

Simplificación [src]

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

(¬x4)∨(x2∧x3)∨(x2∧(¬x1))

Tabla de verdad

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

FND [src]

Ya está reducido a FND

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

(¬x4)∨(x2∧x3)∨(x2∧(¬x1))

FNC [src]

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

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

FNDP [src]

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

(¬x4)∨(x2∧x3)∨(x2∧(¬x1))

FNCD [src]

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

(x2∨(¬x4))∧(x3∨(¬x1)∨(¬x4))

¿Cómo usar?

Expresiones idénticas

Expresión ¬(¬(¬X1∧X2)∧¬X3∨¬(X2∨¬X4))∨¬X4

Solución