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Lógica matemática/ ¬x2∧(¬x1∨x3)∨x1∧x2∧¬x3

Expresión ¬x2∧(¬x1∨x3)∨x1∧x2∧¬x3

El profesor se sorprenderá mucho al ver tu solución correcta😉

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    Solución

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