Sr Examen
Lógica matemática/ NOT(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(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(x)*x3*x4+x1*x*x5+x3*x1*NOT(x4)*NOT(x1)+x2*x4+NOT(x2)*NOT(x3)*x4+x2*x4+(x1*x*x3+1)*(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)∨(x∧x1∧x5)∨(¬(x1∧x2))∨((¬x1)∧(¬x3))∨(x1∧x2∧(¬x5))∨(x3∧x4∧(¬x))∨(x3∧x4∧(¬x1))∨(x3∧(¬x1)∧(¬x4))∨(x4∧(¬x2)∧(¬x3))∨(x1∧x3∧(¬x1)∧(¬x4))
    $$\left(x_{2} \wedge x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x \wedge x_{1} \wedge x_{5}\right) \vee \left(x_{1} \wedge x_{2} \wedge \neg x_{5}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \neg \left(x_{1} \wedge x_{2}\right)$$
    Solución detallada
    $$\neg \left(x_{1} \wedge x_{2}\right) = \neg x_{1} \vee \neg x_{2}$$
    $$x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4} = \text{False}$$
    $$\left(x_{2} \wedge x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(x \wedge x_{1} \wedge x_{5}\right) \vee \left(x_{1} \wedge x_{2} \wedge \neg x_{5}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \neg \left(x_{1} \wedge x_{2}\right) = x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$
    Simplificación [src]
    $$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$ 
    x∨x4∨(¬x1)∨(¬x2)∨(¬x5)
    Tabla de verdad 
    +---+----+----+----+----+----+--------+
| x | x1 | x2 | x3 | x4 | x5 | result |
+===+====+====+====+====+====+========+
| 0 | 0  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 0  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 0  | 1  | 0      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 0  | 1  | 0      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 0 | 1  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 0  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 0  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 0  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 0  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 0  | 1  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 1  | 0  | 1      |
+---+----+----+----+----+----+--------+
| 1 | 1  | 1  | 1  | 1  | 1  | 1      |
+---+----+----+----+----+----+--------+
    FND [src]
    Ya está reducido a FND
    $$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$ 
    x∨x4∨(¬x1)∨(¬x2)∨(¬x5)
    FNDP [src]
    $$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$ 
    x∨x4∨(¬x1)∨(¬x2)∨(¬x5)
    FNCD [src]
    $$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$ 
    x∨x4∨(¬x1)∨(¬x2)∨(¬x5)
    FNC [src]
    Ya está reducido a FNC
    $$x \vee x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{5}$$ 
    x∨x4∨(¬x1)∨(¬x2)∨(¬x5)
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