Sr Examen
Lógica matemática/
¬x1¬x2¬x3¬x4∨¬x1x2¬x3¬x4∨¬x1¬x2x3¬x4∨x1¬x2x3¬x4∨¬x1x2x3¬x4∨¬x1x2¬x3x4∨x1x2¬x3x4∨¬x1¬x2x3x4∨x1¬x2x3x4∨¬x1x2x3x4
Expresión ¬x1¬x2¬x3¬x4∨¬x1x2¬x3¬x4∨¬x1¬x2x3¬x4∨x1¬x2x3¬x4∨¬x1x2x3¬x4∨¬x1x2¬x3x4∨x1x2¬x3x4∨¬x1¬x2x3x4∨x1¬x2x3x4∨¬x1x2x3x4
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
(x1∧x2∧x4∧(¬x3))∨(x1∧x3∧x4∧(¬x2))∨(x2∧x3∧x4∧(¬x1))∨(x1∧x3∧(¬x2)∧(¬x4))∨(x2∧x3∧(¬x1)∧(¬x4))∨(x2∧x4∧(¬x1)∧(¬x3))∨(x3∧x4∧(¬x1)∧(¬x2))∨(x2∧(¬x1)∧(¬x3)∧(¬x4))∨(x3∧(¬x1)∧(¬x2)∧(¬x4))∨((¬x1)∧(¬x2)∧(¬x3)∧(¬x4))
$$\left(x_{1} \wedge x_{2} \wedge x_{4} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{4} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{2} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge \neg x_{1} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right)$$
Solución detallada
$$\left(x_{1} \wedge x_{2} \wedge x_{4} \wedge \neg x_{3}\right) \vee \left(x_{1} \wedge x_{3} \wedge x_{4} \wedge \neg x_{2}\right) \vee \left(x_{1} \wedge x_{3} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{3} \wedge x_{4} \wedge \neg x_{1}\right) \vee \left(x_{2} \wedge x_{3} \wedge \neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge \neg x_{1} \wedge \neg x_{3}\right) \vee \left(x_{2} \wedge \neg x_{1} \wedge \neg x_{3} \wedge \neg x_{4}\right) \vee \left(x_{3} \wedge x_{4} \wedge \neg x_{1} \wedge \neg x_{2}\right) \vee \left(x_{3} \wedge \neg x_{1} \wedge \neg x_{2} \wedge \neg x_{4}\right) \vee \left(\neg x_{1} \wedge \neg x_{2} \wedge \neg x_{3} \wedge \neg x_{4}\right) = \left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{2}\right) \vee \left(\neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge \neg x_{3}\right)$$
Simplificación
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$$\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{2}\right) \vee \left(\neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge \neg x_{3}\right)$$
(x2∧(¬x1))∨(x3∧(¬x2))∨((¬x1)∧(¬x4))∨(x2∧x4∧(¬x3))
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 | 1 | +----+----+----+----+--------+ | 0 | 1 | 0 | 0 | 1 | +----+----+----+----+--------+ | 0 | 1 | 0 | 1 | 1 | +----+----+----+----+--------+ | 0 | 1 | 1 | 0 | 1 | +----+----+----+----+--------+ | 0 | 1 | 1 | 1 | 1 | +----+----+----+----+--------+ | 1 | 0 | 0 | 0 | 0 | +----+----+----+----+--------+ | 1 | 0 | 0 | 1 | 0 | +----+----+----+----+--------+ | 1 | 0 | 1 | 0 | 1 | +----+----+----+----+--------+ | 1 | 0 | 1 | 1 | 1 | +----+----+----+----+--------+ | 1 | 1 | 0 | 0 | 0 | +----+----+----+----+--------+ | 1 | 1 | 0 | 1 | 1 | +----+----+----+----+--------+ | 1 | 1 | 1 | 0 | 0 | +----+----+----+----+--------+ | 1 | 1 | 1 | 1 | 0 | +----+----+----+----+--------+
FNC
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$$\left(x_{2} \vee x_{3} \vee \neg x_{1}\right) \wedge \left(x_{2} \vee x_{3} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee \neg x_{2} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee x_{4} \vee \neg x_{1}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{3}\right) \wedge \left(x_{4} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(\neg x_{1} \vee \neg x_{2} \vee \neg x_{3}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{4} \vee \neg x_{1}\right) \wedge \left(x_{2} \vee x_{3} \vee x_{4} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee x_{3} \vee \neg x_{1} \vee \neg x_{3}\right) \wedge \left(x_{2} \vee x_{3} \vee \neg x_{1} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee x_{3} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee x_{4} \vee \neg x_{1} \vee \neg x_{2}\right) \wedge \left(x_{2} \vee x_{4} \vee \neg x_{2} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{3}\right) \wedge \left(x_{2} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{4}\right) \wedge \left(x_{2} \vee \neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee x_{4} \vee \neg x_{1} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee \neg x_{1} \vee \neg x_{3} \vee \neg x_{4}\right) \wedge \left(x_{4} \vee \neg x_{1} \vee \neg x_{2} \vee \neg x_{4}\right) \wedge \left(\neg x_{1} \vee \neg x_{2} \vee \neg x_{3} \vee \neg x_{4}\right)$$
(x2∨x3∨(¬x1))∧(x2∨x3∨(¬x4))∧(x3∨x4∨(¬x1))∧(x2∨(¬x1)∨(¬x2))∧(x2∨(¬x2)∨(¬x4))∧(x3∨(¬x1)∨(¬x3))∧(x4∨(¬x1)∨(¬x2))∧(x2∨x3∨x4∨(¬x1))∧(x2∨x3∨x4∨(¬x4))∧((¬x1)∨(¬x2)∨(¬x3))∧(x2∨x3∨(¬x1)∨(¬x3))∧(x2∨x3∨(¬x1)∨(¬x4))∧(x2∨x3∨(¬x3)∨(¬x4))∧(x2∨x4∨(¬x1)∨(¬x2))∧(x2∨x4∨(¬x2)∨(¬x4))∧(x3∨x4∨(¬x1)∨(¬x4))∧(x2∨(¬x1)∨(¬x2)∨(¬x3))∧(x2∨(¬x1)∨(¬x2)∨(¬x4))∧(x2∨(¬x2)∨(¬x3)∨(¬x4))∧(x3∨(¬x1)∨(¬x3)∨(¬x4))∧(x4∨(¬x1)∨(¬x2)∨(¬x4))∧((¬x1)∨(¬x2)∨(¬x3)∨(¬x4))
FND
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Ya está reducido a FND
$$\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{2}\right) \vee \left(\neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge \neg x_{3}\right)$$
(x2∧(¬x1))∨(x3∧(¬x2))∨((¬x1)∧(¬x4))∨(x2∧x4∧(¬x3))
FNDP
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$$\left(x_{2} \wedge \neg x_{1}\right) \vee \left(x_{3} \wedge \neg x_{2}\right) \vee \left(\neg x_{1} \wedge \neg x_{4}\right) \vee \left(x_{2} \wedge x_{4} \wedge \neg x_{3}\right)$$
(x2∧(¬x1))∨(x3∧(¬x2))∨((¬x1)∧(¬x4))∨(x2∧x4∧(¬x3))
FNCD
[src]
$$\left(x_{2} \vee x_{3} \vee \neg x_{4}\right) \wedge \left(x_{3} \vee x_{4} \vee \neg x_{1}\right) \wedge \left(\neg x_{1} \vee \neg x_{2} \vee \neg x_{3}\right)$$
(x2∨x3∨(¬x4))∧(x3∨x4∨(¬x1))∧((¬x1)∨(¬x2)∨(¬x3))