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Lógica matemática/ NOT(x2)*x3*x4+x1*x2*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x2*x3+x1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)

Expresión NOT(x2)*x3*x4+x1*x2*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x2*x3+x1)*(NOT(x1)*NOT(x3)+NOT(x1)*x3*x4+NOT(x1)*x3*NOT(x4)+NOT(x1)*NOT(x3))+NOT(x1*x2)+x1*x2*NOT(x5)

El profesor se sorprenderá mucho al ver tu solución correcta😉

⌨

    Solución

    Ha introducido [src] 
    (x2∧x4)∨(x1∧x2∧x5)∨(¬(x1∧x2))∨(x1∧x2∧(¬x5))∨(x3∧x4∧(¬x2))∨(x4∧(¬x2)∧(¬x3))∨(x1∧x3∧(¬x1)∧(¬x4))∨((x1∨(x1∧x2∧x3))∧(((¬x1)∧(¬x3))∨(x3∧x4∧(¬x1))∨(x3∧(¬x1)∧(¬x4))))
    $$\left(x_{2} \wedge x_{4}\right) \vee \left(\left(x_{1} \vee \left(x_{1} \wedge x_{2} \wedge x_{3}\right)\right) \wedge \left(\left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right)\right)\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5}\right) \vee \left(x_{1} \wedge x_{2} \wedge \neg x_{5}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{2}\right) \vee \left(x_{4} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \neg \left(x_{1} \wedge x_{2}\right)$$
    Solución detallada
    $$\neg \left(x_{1} \wedge x_{2}\right) = \neg x_{1} \vee \neg x_{2}$$
    $$x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4} = \text{False}$$
    $$x_{1} \vee \left(x_{1} \wedge x_{2} \wedge x_{3}\right) = x_{1}$$
    $$\left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) = \neg x_{1}$$
    $$\left(x_{1} \vee \left(x_{1} \wedge x_{2} \wedge x_{3}\right)\right) \wedge \left(\left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right)\right) = \text{False}$$
    $$\left(x_{2} \wedge x_{4}\right) \vee \left(\left(x_{1} \vee \left(x_{1} \wedge x_{2} \wedge x_{3}\right)\right) \wedge \left(\left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right)\right)\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5}\right) \vee \left(x_{1} \wedge x_{2} \wedge \neg x_{5}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{2}\right) \vee \left(x_{4} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \neg \left(x_{1} \wedge x_{2}\right) = 1$$
    Simplificación [src]
    1 
    1
    Tabla de verdad 
    +----+----+----+----+----+--------+
| x1 | x2 | x3 | x4 | x5 | result |
+====+====+====+====+====+========+
| 0  | 0  | 0  | 0  | 0  | 1      |
+----+----+----+----+----+--------+
| 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  | 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      |
+----+----+----+----+----+--------+
    FNDP [src]
    1 
    1
    FND [src]
    Ya está reducido a FND
    1 
    1
    FNC [src]
    Ya está reducido a FNC
    1 
    1
    FNCD [src]
    1 
    1
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