№4. Даны множества A = {1;2;3;...;20}, B = {3; 6; 9; ...; 27; 30} и C = {1; 3; 5; 7; ...; 29; 31}. Найдите: 1) A ∪ B 2) B ∩ C 3) A ∩ (B ∩ C) 4) B ∩ (A ∩ C) 5) A ∩ (B ∩ C) 6) B ∩ (A ∪ C) 7) A ∩ (B ∪ C) 8) (A ∪ B) ∩ (B ∪ C)

Для решения задачи, сначала определим множества A, B, и C полностью: * A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} * B = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30} * C = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31} Теперь решим каждую часть задачи: 1) **A ∪ B** - объединение множеств A и B, то есть все элементы из A и B без повторений. A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 27, 30} 2) **B ∩ C** - пересечение множеств B и C, то есть элементы, общие для B и C. B ∩ C = {3, 9, 15, 21, 27} 3) **A ∩ (B ∩ C)** - пересечение множества A и результата пересечения B и C. A ∩ (B ∩ C) = {3, 9, 15} 4) **B ∩ (A ∩ C)** - пересечение множества B и результата пересечения A и C. Сначала найдем A ∩ C = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}. B ∩ (A ∩ C) = {3, 9, 15} 5) **A ∩ (B ∩ C)** - пересечение множества A и результата пересечения B и C. (Повторение пункта 3) A ∩ (B ∩ C) = {3, 9, 15} 6) **B ∩ (A ∪ C)** - пересечение множества B и результата объединения A и C. A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 25, 27, 29, 31} B ∩ (A ∪ C) = {3, 6, 9, 12, 15, 18, 21, 27} 7) **A ∩ (B ∪ C)** - пересечение множества A и результата объединения B и C. B ∪ C = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31} A ∩ (B ∪ C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} ∩ {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31} A ∩ (B ∪ C) = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19} 8) **(A ∪ B) ∩ (B ∪ C)** - пересечение результата объединения A и B, и результата объединения B и C. (A ∪ B) ∩ (B ∪ C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 27, 30} ∩ {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 23, 24, 25, 27, 29, 30, 31} (A ∪ B) ∩ (B ∪ C) = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 24, 27, 30} **Ответ:** 1) A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 24, 27, 30} 2) B ∩ C = {3, 9, 15, 21, 27} 3) A ∩ (B ∩ C) = {3, 9, 15} 4) B ∩ (A ∩ C) = {3, 9, 15} 5) A ∩ (B ∩ C) = {3, 9, 15} 6) B ∩ (A ∪ C) = {3, 6, 9, 12, 15, 18, 21, 27} 7) A ∩ (B ∪ C) = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19} 8) (A ∪ B) ∩ (B ∪ C) = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19, 21, 24, 27, 30}