Expresión ¬(x2x3x4)↔¬(x1vx2)←x3|x4⊕x1→x3⊕x4

Ha introducido [src]

x4⊕(x1⇒x3)⊕(((¬(x2∧x3∧x4))⇔(x3⇒(¬(x1∨x2))))|x4)

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

Solución detallada

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

Simplificación [src]

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

x1∧(x4∨(¬x3))∧((¬x2)∨(¬x3))

Tabla de verdad

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

FNDP [src]

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

(x1∧(¬x3))∨(x1∧x4∧(¬x2))

FND [src]

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

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

FNC [src]

Ya está reducido a FNC

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

x1∧(x4∨(¬x3))∧((¬x2)∨(¬x3))

FNCD [src]

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

x1∧(x4∨(¬x3))∧((¬x2)∨(¬x3))

¿Cómo usar?

Expresiones idénticas

Expresión ¬(x2x3x4)↔¬(x1vx2)←x3|x4⊕x1→x3⊕x4

Solución