Sr Examen
Expresión ¬(¬(X1∨¬X2)∨¬X1∧X3∨X2)
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
¬(x2∨(x3∧(¬x1))∨(¬(x1∨(¬x2))))
$$\neg \left(x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right) \vee \neg \left(x_{1} \vee \neg x_{2}\right)\right)$$
Solución detallada
$$\neg \left(x_{1} \vee \neg x_{2}\right) = x_{2} \wedge \neg x_{1}$$
$$x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right) \vee \neg \left(x_{1} \vee \neg x_{2}\right) = x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right)$$
$$\neg \left(x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right) \vee \neg \left(x_{1} \vee \neg x_{2}\right)\right) = \neg x_{2} \wedge \left(x_{1} \vee \neg x_{3}\right)$$
$$x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right) \vee \neg \left(x_{1} \vee \neg x_{2}\right) = x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right)$$
$$\neg \left(x_{2} \vee \left(x_{3} \wedge \neg x_{1}\right) \vee \neg \left(x_{1} \vee \neg x_{2}\right)\right) = \neg x_{2} \wedge \left(x_{1} \vee \neg x_{3}\right)$$
Tabla de verdad
+----+----+----+--------+ | x1 | x2 | x3 | result | +====+====+====+========+ | 0 | 0 | 0 | 1 | +----+----+----+--------+ | 0 | 0 | 1 | 0 | +----+----+----+--------+ | 0 | 1 | 0 | 0 | +----+----+----+--------+ | 0 | 1 | 1 | 0 | +----+----+----+--------+ | 1 | 0 | 0 | 1 | +----+----+----+--------+ | 1 | 0 | 1 | 1 | +----+----+----+--------+ | 1 | 1 | 0 | 0 | +----+----+----+--------+ | 1 | 1 | 1 | 0 | +----+----+----+--------+
FNC
[src]
Ya está reducido a FNC
$$\neg x_{2} \wedge \left(x_{1} \vee \neg x_{3}\right)$$
(¬x2)∧(x1∨(¬x3))
FND
[src]
$$\left(x_{1} \wedge \neg x_{2}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$
(x1∧(¬x2))∨((¬x2)∧(¬x3))
FNDP
[src]
$$\left(x_{1} \wedge \neg x_{2}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right)$$
(x1∧(¬x2))∨((¬x2)∧(¬x3))