Sr Examen
Expresión ¬(¬X1X2⊕X3X4)X5
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
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x5∧(¬((x3∧x4)⊕(x2∧(¬x1))))
$$x_{5} \wedge \neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(x_{2} \wedge \neg x_{1}\right)\right)$$
Вы использовали:
⊕ - Сложение по модулю 2 (Исключающее или).
Возможно вы имели ввиду символ ∨ - Дизъюнкция (ИЛИ)?
Посмотреть с символом ∨
Solución detallada
$$\left(x_{3} \wedge x_{4}\right) ⊕ \left(x_{2} \wedge \neg x_{1}\right) = \left(x_{2} \vee x_{3}\right) \wedge \left(x_{2} \vee x_{4}\right) \wedge \left(x_{3} \vee \neg x_{1}\right) \wedge \left(x_{4} \vee \neg x_{1}\right) \wedge \left(x_{1} \vee \neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
$$\neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(x_{2} \wedge \neg x_{1}\right)\right) = \left(x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge \neg x_{1}\right)$$
$$x_{5} \wedge \neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(x_{2} \wedge \neg x_{1}\right)\right) = x_{5} \wedge \left(x_{1} \vee x_{3} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee x_{4} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right)$$
$$\neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(x_{2} \wedge \neg x_{1}\right)\right) = \left(x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge \neg x_{4}\right) \vee \left(\neg x_{2} \wedge \neg x_{3}\right) \vee \left(\neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge \neg x_{1}\right)$$
$$x_{5} \wedge \neg \left(\left(x_{3} \wedge x_{4}\right) ⊕ \left(x_{2} \wedge \neg x_{1}\right)\right) = x_{5} \wedge \left(x_{1} \vee x_{3} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee x_{4} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right)$$
Simplificación
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$$x_{5} \wedge \left(x_{1} \vee x_{3} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee x_{4} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right)$$
x5∧(x1∨x3∨(¬x2))∧(x1∨x4∨(¬x2))∧(x2∨(¬x3)∨(¬x4))∧((¬x1)∨(¬x3)∨(¬x4))
Tabla de verdad
+----+----+----+----+----+--------+ | x1 | x2 | x3 | x4 | x5 | result | +====+====+====+====+====+========+ | 0 | 0 | 0 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 0 | 0 | 0 | 1 | 1 | +----+----+----+----+----+--------+ | 0 | 0 | 0 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 0 | 0 | 1 | 1 | 1 | +----+----+----+----+----+--------+ | 0 | 0 | 1 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 0 | 1 | 0 | 1 | 1 | +----+----+----+----+----+--------+ | 0 | 0 | 1 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 0 | 1 | 1 | 1 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 0 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 0 | 0 | 1 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 0 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 0 | 1 | 1 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 1 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 1 | 0 | 1 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 1 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 0 | 1 | 1 | 1 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 0 | 0 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 0 | 0 | 0 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 0 | 0 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 0 | 0 | 1 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 0 | 1 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 0 | 1 | 0 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 0 | 1 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 0 | 1 | 1 | 1 | 0 | +----+----+----+----+----+--------+ | 1 | 1 | 0 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 1 | 0 | 0 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 1 | 0 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 1 | 0 | 1 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 1 | 1 | 0 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 1 | 1 | 0 | 1 | 1 | +----+----+----+----+----+--------+ | 1 | 1 | 1 | 1 | 0 | 0 | +----+----+----+----+----+--------+ | 1 | 1 | 1 | 1 | 1 | 0 | +----+----+----+----+----+--------+
FNCD
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$$x_{5} \wedge \left(x_{1} \vee x_{3} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee x_{4} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right)$$
x5∧(x1∨x3∨(¬x2))∧(x1∨x4∨(¬x2))∧(x2∨(¬x3)∨(¬x4))∧((¬x1)∨(¬x3)∨(¬x4))
FNC
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Ya está reducido a FNC
$$x_{5} \wedge \left(x_{1} \vee x_{3} \vee \neg x_{2}\right) \wedge \left(x_{1} \vee x_{4} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right)$$
x5∧(x1∨x3∨(¬x2))∧(x1∨x4∨(¬x2))∧(x2∨(¬x3)∨(¬x4))∧((¬x1)∨(¬x3)∨(¬x4))
FNDP
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$$\left(x_{1} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1}\right)$$
(x1∧x5∧(¬x3))∨(x1∧x5∧(¬x4))∨(x5∧(¬x2)∧(¬x3))∨(x5∧(¬x2)∧(¬x4))∨(x2∧x3∧x4∧x5∧(¬x1))
FND
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$$\left(x_{1} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{5} \wedge \neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{2} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{1} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge x_{5} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{3} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{3}\right) \vee \left(x_{4} \wedge x_{5} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{4} \wedge x_{5} \wedge \neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right)$$
(x1∧x5∧(¬x3))∨(x1∧x5∧(¬x4))∨(x5∧(¬x2)∧(¬x3))∨(x5∧(¬x2)∧(¬x4))∨(x1∧x2∧x5∧(¬x1))∨(x1∧x2∧x5∧(¬x3))∨(x1∧x2∧x5∧(¬x4))∨(x1∧x3∧x5∧(¬x3))∨(x1∧x3∧x5∧(¬x4))∨(x1∧x4∧x5∧(¬x3))∨(x1∧x4∧x5∧(¬x4))∨(x3∧x4∧x5∧(¬x3))∨(x3∧x4∧x5∧(¬x4))∨(x1∧x5∧(¬x1)∧(¬x3))∨(x1∧x5∧(¬x1)∧(¬x4))∨(x1∧x5∧(¬x2)∧(¬x3))∨(x1∧x5∧(¬x2)∧(¬x4))∨(x1∧x5∧(¬x3)∧(¬x4))∨(x2∧x5∧(¬x1)∧(¬x2))∨(x2∧x5∧(¬x2)∧(¬x3))∨(x2∧x5∧(¬x2)∧(¬x4))∨(x3∧x5∧(¬x2)∧(¬x3))∨(x3∧x5∧(¬x2)∧(¬x4))∨(x4∧x5∧(¬x2)∧(¬x3))∨(x4∧x5∧(¬x2)∧(¬x4))∨(x1∧x2∧x3∧x5∧(¬x1))∨(x1∧x2∧x3∧x5∧(¬x3))∨(x1∧x2∧x3∧x5∧(¬x4))∨(x1∧x2∧x4∧x5∧(¬x1))∨(x1∧x2∧x4∧x5∧(¬x3))∨(x1∧x2∧x4∧x5∧(¬x4))∨(x2∧x3∧x4∧x5∧(¬x1))∨(x2∧x3∧x4∧x5∧(¬x3))∨(x2∧x3∧x4∧x5∧(¬x4))∨(x5∧(¬x1)∧(¬x2)∧(¬x3))∨(x5∧(¬x1)∧(¬x2)∧(¬x4))∨(x5∧(¬x2)∧(¬x3)∧(¬x4))∨(x1∧x2∧x5∧(¬x1)∧(¬x2))∨(x1∧x2∧x5∧(¬x2)∧(¬x3))∨(x1∧x2∧x5∧(¬x2)∧(¬x4))∨(x1∧x3∧x5∧(¬x1)∧(¬x3))∨(x1∧x3∧x5∧(¬x1)∧(¬x4))∨(x1∧x3∧x5∧(¬x3)∧(¬x4))∨(x1∧x4∧x5∧(¬x1)∧(¬x3))∨(x1∧x4∧x5∧(¬x1)∧(¬x4))∨(x1∧x4∧x5∧(¬x3)∧(¬x4))∨(x2∧x3∧x5∧(¬x1)∧(¬x2))∨(x2∧x3∧x5∧(¬x2)∧(¬x3))∨(x2∧x3∧x5∧(¬x2)∧(¬x4))∨(x2∧x4∧x5∧(¬x1)∧(¬x2))∨(x2∧x4∧x5∧(¬x2)∧(¬x3))∨(x2∧x4∧x5∧(¬x2)∧(¬x4))∨(x3∧x4∧x5∧(¬x1)∧(¬x3))∨(x3∧x4∧x5∧(¬x1)∧(¬x4))∨(x3∧x4∧x5∧(¬x3)∧(¬x4))∨(x1∧x5∧(¬x1)∧(¬x2)∧(¬x3))∨(x1∧x5∧(¬x1)∧(¬x2)∧(¬x4))∨(x1∧x5∧(¬x2)∧(¬x3)∧(¬x4))∨(x3∧x5∧(¬x1)∧(¬x2)∧(¬x3))∨(x3∧x5∧(¬x1)∧(¬x2)∧(¬x4))∨(x3∧x5∧(¬x2)∧(¬x3)∧(¬x4))∨(x4∧x5∧(¬x1)∧(¬x2)∧(¬x3))∨(x4∧x5∧(¬x1)∧(¬x2)∧(¬x4))∨(x4∧x5∧(¬x2)∧(¬x3)∧(¬x4))