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Консультация № 174979
07.12.2009, 13:19
35.00 руб.
0
4
1
выяснить является ли полной система σ={x→y,¬(xΘyΘz)} где Θ-сумма по модулю два
Обсуждение
07.12.2009, 14:09
общий
это ответ
Здравствуйте, Кусмарцев Андрей Валерьевич.
Для того, чтобы система функций была полной, необходимо и достаточно, чтобы
1) она содержала хотя бы одну функцию, не сохраняющую 0
x→y не сохраняет 0, 0→0 равно 1
2) хотя бы одну функцию, , не сохраняющую 1
¬(xΘyΘz)=0 при x=y=z=1
3) хотя бы одну несамодвойственную функцию
x→y не самодвойственна
4) хотя бы одну немонотонную функцию
x→y немонотонная
5) хотя бы одну нелинейную функцию
x→y нелинейная
Следовательно, наша система полная.
Для того, чтобы система функций была полной, необходимо и достаточно, чтобы
1) она содержала хотя бы одну функцию, не сохраняющую 0
x→y не сохраняет 0, 0→0 равно 1
2) хотя бы одну функцию, , не сохраняющую 1
¬(xΘyΘz)=0 при x=y=z=1
3) хотя бы одну несамодвойственную функцию
x→y не самодвойственна
4) хотя бы одну немонотонную функцию
x→y немонотонная
5) хотя бы одну нелинейную функцию
x→y нелинейная
Следовательно, наша система полная.
3
07.12.2009, 14:48
общий
Кусмарцев Андрей Валерьевич:
Чем Вас не удовлетворил ответ? Я могу разъяснить подробности.
Чем Вас не удовлетворил ответ? Я могу разъяснить подробности.
Неизвестный
07.12.2009, 15:18
общий
отсутсвие подробного решения(приходится верить на слово) я про 3,4,5
07.12.2009, 15:42
общий
Кусмарцев Андрей Валерьевич:
самодвойственная функция - двойственная сама себе. Двойственная функция - эта та, которая получается заменой аргументов на их отрицание и последующим отрицанием результата.
у импликации, например значения 1 1 0 1. Через конъюнкцию и дизъюнкцию она выражается как ¬x[$8743$]y
Двойственная ей функция будет 0 1 0 0. x[$8744$]¬y.
x→y немонотонная, так как f(0,0)=1, а f(1,0)=0.
И x→y нелинейная, так как ее нельзя выразить через сложение по модулю 2.
самодвойственная функция - двойственная сама себе. Двойственная функция - эта та, которая получается заменой аргументов на их отрицание и последующим отрицанием результата.
у импликации, например значения 1 1 0 1. Через конъюнкцию и дизъюнкцию она выражается как ¬x[$8743$]y
Двойственная ей функция будет 0 1 0 0. x[$8744$]¬y.
x→y немонотонная, так как f(0,0)=1, а f(1,0)=0.
И x→y нелинейная, так как ее нельзя выразить через сложение по модулю 2.
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