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Консультация № 199913
19.12.2020, 07:39
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Уважаемые эксперты!помогите! Найти число булевых функций от n переменных, сохраняющих 1. жаемые эксперты! Пожалуйста
Обсуждение
23.12.2020, 04:45
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это ответ
Здравствуйте, lubovaleksandrovna463!
Каждая булева функция определяется своим столбцом значений. При этом каждый элемент столбца соответствует двоичному вектору длины n (содержащему значения n переменных). Число различных двоичных векторв длины n равно 2[sup]n[/sup], поэтому столбец значений функции n переменных есть двоичный вектор длины 2[sup]n[/sup]. Аналогично, число различных двоичных векторов длины 2[sup]n[/sup] (а значит и булевых функций n переменных) равно
. Значение функции на наборе из всех единиц задаёт последняя компонента соответствуюшего ей вектора. Так как ровно половина векторов содержит в последней компоненте единицу, то число функций, сохраняющих константу 1, равно
Каждая булева функция определяется своим столбцом значений. При этом каждый элемент столбца соответствует двоичному вектору длины n (содержащему значения n переменных). Число различных двоичных векторв длины n равно 2[sup]n[/sup], поэтому столбец значений функции n переменных есть двоичный вектор длины 2[sup]n[/sup]. Аналогично, число различных двоичных векторов длины 2[sup]n[/sup] (а значит и булевых функций n переменных) равно
. Значение функции на наборе из всех единиц задаёт последняя компонента соответствуюшего ей вектора. Так как ровно половина векторов содержит в последней компоненте единицу, то число функций, сохраняющих константу 1, равно
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