Sr Examen
Expresión не(x1*x2+x3*x4)*x1+не(x2*неx3+x4)
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(¬(x4∨(x2∧(¬x3))))∨(x1∧(¬((x1∧x2)∨(x3∧x4))))
$$\left(x_{1} \wedge \neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right)\right) \vee \neg \left(x_{4} \vee \left(x_{2} \wedge \neg x_{3}\right)\right)$$
Solución detallada
$$\neg \left(x_{4} \vee \left(x_{2} \wedge \neg x_{3}\right)\right) = \neg x_{4} \wedge \left(x_{3} \vee \neg x_{2}\right)$$
$$\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right) = \left(x_{1} \vee x_{3}\right) \wedge \left(x_{1} \vee x_{4}\right) \wedge \left(x_{2} \vee x_{3}\right) \wedge \left(x_{2} \vee x_{4}\right)$$
$$\neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right) = \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(\neg x_{1} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{4}\right)$$
$$x_{1} \wedge \neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right) = x_{1} \wedge \neg x_{2} \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
$$\left(x_{1} \wedge \neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right)\right) \vee \neg \left(x_{4} \vee \left(x_{2} \wedge \neg x_{3}\right)\right) = \left(x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
$$\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right) = \left(x_{1} \vee x_{3}\right) \wedge \left(x_{1} \vee x_{4}\right) \wedge \left(x_{2} \vee x_{3}\right) \wedge \left(x_{2} \vee x_{4}\right)$$
$$\neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right) = \left(\neg x_{1} \wedge \neg x_{3}\right) \vee \left(\neg x_{1} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{4}\right)$$
$$x_{1} \wedge \neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right) = x_{1} \wedge \neg x_{2} \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
$$\left(x_{1} \wedge \neg \left(\left(x_{1} \wedge x_{2}\right) \vee \left(x_{3} \wedge x_{4}\right)\right)\right) \vee \neg \left(x_{4} \vee \left(x_{2} \wedge \neg x_{3}\right)\right) = \left(x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
Simplificación
[src]
$$\left(x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
(x1∨(¬x4))∧(x3∨(¬x2))∧((¬x3)∨(¬x4))
Tabla de verdad
+----+----+----+----+--------+ | x1 | x2 | x3 | x4 | result | +====+====+====+====+========+ | 0 | 0 | 0 | 0 | 1 | +----+----+----+----+--------+ | 0 | 0 | 0 | 1 | 0 | +----+----+----+----+--------+ | 0 | 0 | 1 | 0 | 1 | +----+----+----+----+--------+ | 0 | 0 | 1 | 1 | 0 | +----+----+----+----+--------+ | 0 | 1 | 0 | 0 | 0 | +----+----+----+----+--------+ | 0 | 1 | 0 | 1 | 0 | +----+----+----+----+--------+ | 0 | 1 | 1 | 0 | 1 | +----+----+----+----+--------+ | 0 | 1 | 1 | 1 | 0 | +----+----+----+----+--------+ | 1 | 0 | 0 | 0 | 1 | +----+----+----+----+--------+ | 1 | 0 | 0 | 1 | 1 | +----+----+----+----+--------+ | 1 | 0 | 1 | 0 | 1 | +----+----+----+----+--------+ | 1 | 0 | 1 | 1 | 0 | +----+----+----+----+--------+ | 1 | 1 | 0 | 0 | 0 | +----+----+----+----+--------+ | 1 | 1 | 0 | 1 | 0 | +----+----+----+----+--------+ | 1 | 1 | 1 | 0 | 1 | +----+----+----+----+--------+ | 1 | 1 | 1 | 1 | 0 | +----+----+----+----+--------+
FNDP
[src]
$$\left(x_{3} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{3}\right)$$
(x3∧(¬x4))∨((¬x2)∧(¬x4))∨(x1∧(¬x2)∧(¬x3))
FNC
[src]
Ya está reducido a FNC
$$\left(x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
(x1∨(¬x4))∧(x3∨(¬x2))∧((¬x3)∨(¬x4))
FNCD
[src]
$$\left(x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{2}\right) \wedge \left(\neg x_{3} \vee \neg x_{4}\right)$$
(x1∨(¬x4))∧(x3∨(¬x2))∧((¬x3)∨(¬x4))
FND
[src]
$$\left(x_{3} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right)$$
(x3∧(¬x4))∨((¬x2)∧(¬x4))∨(x1∧x3∧(¬x3))∨(x1∧x3∧(¬x4))∨(x1∧(¬x2)∧(¬x3))∨(x1∧(¬x2)∧(¬x4))∨(x3∧(¬x3)∧(¬x4))∨((¬x2)∧(¬x3)∧(¬x4))