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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Между элементами множеств X и Y задано соответствие R. 1.Задате соответствие R графом, множеством пар, графиком. 2. Укажите вид соответствия. X = {2,3,4,5} , Y = {2,3,6,9} R - "числа x и y при делении на 3 дают одинаковый остаток"
Я предлагаю Вам сначала указать остатки от деления на чисел, являющихся элементами множеств и Например, при делении числа на число получим
то есть остаток от деления равен при делении числа на число получим
то есть остаток от деления равен
Выполнив это, Вы получите, что при делении на число -- среди элементов множества число даёт остаток, равный число даёт остаток, равный числа дают остаток, равный -- среди элементов множества числа дают остаток, равный число даёт остаток, равный Следовательно, отношение задаётся следующим множеством пар:
Чтобы задать это отношение в виде графа, нужно нарисовать два овала. Внутри одного овала четырьмя точками изобразить элементы множества внутри второго овала четырьмя точками изобразить элементы множества От точки, соответствующей элементу в первом овале, провести дуги, заканчивающиеся стрелками, к точкам, соответствующим элементам во втором овале. От точки, соответствующей элементу в первом овале, провести дугу, заканчивающуюся стрелкой, к точке соответствующей элементу во втором овале. От точки, соответствующей элементу в первом овале, провести дугу, заканчивающуюся стрелкой, к точке соответствующей элементу во втором овале. Похожие изображения показаны на рисунках 67, 68 здесь.
Чтобы задать это отношение в виде графика, нужно показать на координатной плоскости точки, которые имеют координаты Похожее изображение показано на рисунке 69 там же.
Что касается вида соответствия, то, по-моему, заданное соответствие не является ни однозначным, ни функциональным.
Об авторе:
Facta loquuntur.
Форма ответа
Отправка постов/ответов доступна только зарегистрированным и подтвержденным пользователям.
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