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Консультация № 191985
04.12.2017, 07:55
0.00 руб.
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Сколько существует различных наборов значений логических переменных x1,x2,x3,x4,x5,x6,x7,x8,x9,x10, которые удовлетворяют всем перечисленным ниже условиям?
(x1 → x2) xor (x3 → x4) = 1
(x3 → x4) xor (x5 → x6) = 1
(x5 → x6) xor (x7 → x8) = 1
(x7 → x8) xor (x9 → x10) = 1
Приведите полное решение задачи с пояснениями.
Сколько существует различных наборов значений логических переменных x1,x2,x3,x4,x5,x6,x7,x8,x9,x10, которые удовлетворяют всем перечисленным ниже условиям?
(x1 → x2) xor (x3 → x4) = 1
(x3 → x4) xor (x5 → x6) = 1
(x5 → x6) xor (x7 → x8) = 1
(x7 → x8) xor (x9 → x10) = 1
Приведите полное решение задачи с пояснениями.
Обсуждение
08.12.2017, 08:15
общий
Адресаты:
Об авторе:
Я только в одном глубоко убеждён - не надо иметь убеждений! :)
Я только в одном глубоко убеждён - не надо иметь убеждений! :)
13.12.2017, 18:31
общий
это ответ
Здравствуйте, IIISergeyIII!
Составим таблицу функции (x[sub]1[/sub][$8594$]x[sub]2[/sub])[$8853$](x[sub]3[/sub][$8594$]x[sub]4[/sub]):
Из неё видно, что первому условию удовлетворяют все наборы вида 0x10xxxxxx, 100xxxxxxx, 1011xxxxxx и 1110xxxxxx, где x - любое значение (всего 128+128+64+64=384 набора). Аналогично, второму условию удовлетворяют все наборы вида xx0x10xxxx, xx100xxxxx, xx1011xxxx и xx1110xxxx. Тогда одновременно первому и второму условию будут удовлетворять следующие наборы: 0x100xxxxx, 0x1011xxxx, 100x10xxxx, 101110xxxx, 11100xxxxx и 111011xxxx (всего 64+32+32+16+32+16=192 набора). Если учесть также наборы, удовлетворяющие третьему условию (xxxx0x10xx, xxxx100xxx, xxxx1011xx и xxxx1110xx), то первым трём условиям будут удовлетворять следующие наборы: 0x100x10xx, 0x101110xx, 100x100xxx, 100x1011xx, 1011100xxx, 10111011xx, 11100x10xx и 11101110xx (всего 16+8+16+8+8+4+8+4=72 набора). Наконец, с учётом наборов, удовлетворяющих четвёртому условию (xxxxxx0x10, xxxxxx100x, xxxxxx1011 и xxxxxx1110), решением будет 0x100x100x, 0x100x1011, 0x1011100x, 0x10111011, 100x100x10, 100x101110, 1011100x10, 1011101110, 11100x100x, 11100x1011, 111011100x, 1110111011 - 8+4+4+2+4+2+2+1+4+2+2+1=36 наборов.
Составим таблицу функции (x[sub]1[/sub][$8594$]x[sub]2[/sub])[$8853$](x[sub]3[/sub][$8594$]x[sub]4[/sub]):
Из неё видно, что первому условию удовлетворяют все наборы вида 0x10xxxxxx, 100xxxxxxx, 1011xxxxxx и 1110xxxxxx, где x - любое значение (всего 128+128+64+64=384 набора). Аналогично, второму условию удовлетворяют все наборы вида xx0x10xxxx, xx100xxxxx, xx1011xxxx и xx1110xxxx. Тогда одновременно первому и второму условию будут удовлетворять следующие наборы: 0x100xxxxx, 0x1011xxxx, 100x10xxxx, 101110xxxx, 11100xxxxx и 111011xxxx (всего 64+32+32+16+32+16=192 набора). Если учесть также наборы, удовлетворяющие третьему условию (xxxx0x10xx, xxxx100xxx, xxxx1011xx и xxxx1110xx), то первым трём условиям будут удовлетворять следующие наборы: 0x100x10xx, 0x101110xx, 100x100xxx, 100x1011xx, 1011100xxx, 10111011xx, 11100x10xx и 11101110xx (всего 16+8+16+8+8+4+8+4=72 набора). Наконец, с учётом наборов, удовлетворяющих четвёртому условию (xxxxxx0x10, xxxxxx100x, xxxxxx1011 и xxxxxx1110), решением будет 0x100x100x, 0x100x1011, 0x1011100x, 0x10111011, 100x100x10, 100x101110, 1011100x10, 1011101110, 11100x100x, 11100x1011, 111011100x, 1110111011 - 8+4+4+2+4+2+2+1+4+2+2+1=36 наборов.
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