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Lógica matemática/ not(x1)¬(x2)v(x2vnot(x3))&(not(x2)vx3)vnot(x3)vnot(x4)

Expresión not(x1)¬(x2)v(x2vnot(x3))&(not(x2)vx3)vnot(x3)vnot(x4)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (¬x3)∨(¬x4)∨((¬x1)∧(¬x2))∨((x2∨(¬x3))∧(x3∨(¬x2)))
    $$\left(\neg x_{1} \wedge \neg x_{2}\right) \vee \left(\left(x_{2} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{2}\right)\right) \vee \neg x_{3} \vee \neg x_{4}$$
    Solución detallada
    $$\left(x_{2} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) = \left(x_{2} \wedge x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$
    $$\left(\neg x_{1} \wedge \neg x_{2}\right) \vee \left(\left(x_{2} \vee \neg x_{3}\right) \wedge \left(x_{3} \vee \neg x_{2}\right)\right) \vee \neg x_{3} \vee \neg x_{4} = x_{2} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}$$
    Simplificación [src]
    $$x_{2} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}$$ 
    x2∨(¬x1)∨(¬x3)∨(¬x4)
    Tabla de verdad 
    +----+----+----+----+--------+
| x1 | x2 | x3 | x4 | result |
+====+====+====+====+========+
| 0  | 0  | 0  | 0  | 1      |
+----+----+----+----+--------+
| 0  | 0  | 0  | 1  | 1      |
+----+----+----+----+--------+
| 0  | 0  | 1  | 0  | 1      |
+----+----+----+----+--------+
| 0  | 0  | 1  | 1  | 1      |
+----+----+----+----+--------+
| 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  | 1      |
+----+----+----+----+--------+
| 1  | 0  | 1  | 0  | 1      |
+----+----+----+----+--------+
| 1  | 0  | 1  | 1  | 0      |
+----+----+----+----+--------+
| 1  | 1  | 0  | 0  | 1      |
+----+----+----+----+--------+
| 1  | 1  | 0  | 1  | 1      |
+----+----+----+----+--------+
| 1  | 1  | 1  | 0  | 1      |
+----+----+----+----+--------+
| 1  | 1  | 1  | 1  | 1      |
+----+----+----+----+--------+
    FNDP [src]
    $$x_{2} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}$$ 
    x2∨(¬x1)∨(¬x3)∨(¬x4)
    FNC [src]
    Ya está reducido a FNC
    $$x_{2} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}$$ 
    x2∨(¬x1)∨(¬x3)∨(¬x4)
    FND [src]
    Ya está reducido a FND
    $$x_{2} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}$$ 
    x2∨(¬x1)∨(¬x3)∨(¬x4)
    FNCD [src]
    $$x_{2} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}$$ 
    x2∨(¬x1)∨(¬x3)∨(¬x4)
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