Тема урока: «Определение количества решений системы логических уравнений»,
Цели:
- Знакомство учащихся с решением систем логических уравнений, методами определения количества решений системы логических уравнений и их использования для решения задач;
- Развитие математического, логического мышления, воображения, умения анализировать, применять ранее полученные знания;
- Воспитание интереса к предмету, внимания.
Оборудование: интерактивный комплекс, материалы ЕГЭ.
Ход урока
- Организационный момент. На уроках математики вы знакомитесь с решением различных уравнений – алгебраических, трансцендентных и т.д. и их систем. Более экзотические – логические уравнения, в которых все величины могут принимать только два значения – «истина (1)» или «ложь (0)». Традиционно эти уравнения тоже относятся к математике, но на практике логические уравнения и их системы оказались полезны при разработке цифровых логических устройств, поэтому в ЕГЭ по информатике появились задания, в которых необходимо решить логическое уравнение или определить количество решений системы логических уравнений.
Наша сегодняшняя задача – научиться определять количество решений системы логических уравнений, в ЕГЭ – это задание В15.
- Актуализация знаний. Давайте вспомним базовые логические операции – инверсия, дизъюнкция и конъюнкция, (обучающиеся дают определения и вспоминают таблицу истинности для этих операций).
Производные от базовых логических функций – исключающее ИЛИ, импликация, эквиваленция.
Вспомним некоторые логические тождества, которые помогут в преобразовании логических уравнений:
![](/2014-2015/otkrur/k1.jpg)
3. Новый материал. Способов решения систем логических уравнений достаточно много:
- Сведение к одному уравнению
- Составление таблицы истинности. Напомню, количество строк таблицы рассчитывается по формуле n=2k, где k – количество логических переменных, в системах количество переменных – до 10 и более, тогда количество строк - >= 1024!
- Декомпозиция. В этом методе фиксируется одна переменная (0 или 1), система за счет этого упрощается, затем фиксируется вторая переменная и т.д. Метод трудоемкий.
- Последовательное решение уравнений.
Количество решений. В задаче 23 ЕГЭ требуется найти количество решений системы логических уравнений.
Задача 1. Найти количество решений системы логических уравнений:
![](/2014-2015/otkrur/k2.jpg)
где x1 … x10 – неизвестные логические величины.
Решение: Несложно заметить, что первое уравнение зависит только от х1 и х2, затем во втором уравнении добавляется х3 и т.д., логично попробовать решать уравнения последовательно, простраивая дерево решений. Первое уравнение обращается в истинное равенство в трех случаях:
![](/2014-2015/otkrur/k3.png)
Количество решений 1-го уравнения – 3. Теперь подключаем второе уравнение. Допустим, что х3 зависит от ранее выбранного значения х2: если х2=0, то х3 может принимать любое значение (0 или 1), а если х2=1, то х3=1.
![](/2014-2015/otkrur/k4.jpg)
Количество решений – 4. Легко заметить, что при добавлении очередного уравнения (и очередной переменной) количество решений увеличивается на 1. Таким образом, система из трех уравнений имеет 5 решений, из четырех – 6, а исходная система из 9 уравнений – 11 решений. Ответ: 11 решений.
Задача 2. Найти количество решений системы логических уравнений:
![](/2014-2015/otkrur/k5.jpg)
Решение: Здесь, так же как и в предыдущей задаче, удобнее всего последовательно решать уравнения. Количество уравнений – 9. Сначала упростим исходные уравнения:
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)
Первое уравнение имеет 6 решений, при добавлении очередной переменной количество решений увеличивается на 2. Последнее 9-ое уравнение выполняется при Х1 не равном Х10, это возможно в двух случаях – крайние ветки, для которых 0=0 И 1= 1, отбрасываем эти два решения, тогда количество решений – 20-2=18. Ответ: 18 решений. |