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Консультация № 198639
19.05.2020, 12:17
0.00 руб.
19.05.2020, 13:58
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
Среди 313 целых чисел, 165 кратно 7, 110 кратно 9, 39 кратно 49, 48 кратно 63, 30 кратно 441. Определить, сколько среди них не кратно 7 или кратно 9.
Среди 313 целых чисел, 165 кратно 7, 110 кратно 9, 39 кратно 49, 48 кратно 63, 30 кратно 441. Определить, сколько среди них не кратно 7 или кратно 9.
Обсуждение
19.05.2020, 21:31
общий
это ответ
Здравствуйте, Анна!
Введём 2 условия
A - число кратно 7
B - число кратно 9
количество чисел, удовлетворяющих условию [$172$]A[$8744$]B (не кратно 7 или кратно 9), представим следующим образом
n([$172$]A[$8744$]B)=n([$172$]A)+n(B)-n([$172$]A[$8743$]B)=m-n(A)+n(B)-(n(B)-n(A[$8743$]B))=m-n(A)+n(A[$8743$]B)
по условию
m=313 (всего чисел)
n(A)=165 (кратно 7)
n(A[$8743$]B)=48 (кратно 7 и кратно 9 - то есть, кратно 63)
n([$172$]A[$8744$]B)=313-165+48=196
Введём 2 условия
A - число кратно 7
B - число кратно 9
количество чисел, удовлетворяющих условию [$172$]A[$8744$]B (не кратно 7 или кратно 9), представим следующим образом
n([$172$]A[$8744$]B)=n([$172$]A)+n(B)-n([$172$]A[$8743$]B)=m-n(A)+n(B)-(n(B)-n(A[$8743$]B))=m-n(A)+n(A[$8743$]B)
по условию
m=313 (всего чисел)
n(A)=165 (кратно 7)
n(A[$8743$]B)=48 (кратно 7 и кратно 9 - то есть, кратно 63)
n([$172$]A[$8744$]B)=313-165+48=196
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