Даны множества: A = (3; 4; 7; 12; 34; 57), B = (2; 3; 4; 5; 11), C = (1; 3; 4; 12; 15; 27). Найдите: 1. A ∩ B; 2. A ∪ B; 3. A ∪ (B ∩ C); 4. (A ∪ B) ∩ C; 5. A ∩ (B ∪ C); 6. (A ∩ B) ∪ C; 7. (A ∪ B) ∩ (B ∪ C); 8. (A ∩ B) ∪ (B ∩ C); 9. (A ∩ C) ∪ (B ∩ C); 10. (A ∪ C) ∩ (B ∪ C).

Сначала найдём пересечения, которые встречаются в выражениях: A ∩ B = {3; 4}, B ∩ C = {3; 4}, A ∩ C = {3; 4; 12}.

1. A ∩ B = {3; 4}.
2. A ∪ B = {2; 3; 4; 5; 7; 11; 12; 34; 57}.
3. A ∪ (B ∩ C) = A ∪ {3; 4} = {3; 4; 7; 12; 34; 57}.
4. (A ∪ B) ∩ C = {3; 4; 12}.
5. A ∩ (B ∪ C) = {3; 4; 12}.
6. (A ∩ B) ∪ C = {3; 4} ∪ C = {1; 3; 4; 12; 15; 27}.
7. (A ∪ B) ∩ (B ∪ C) = {2; 3; 4; 5; 11; 12}.
8. (A ∩ B) ∪ (B ∩ C) = {3; 4} ∪ {3; 4} = {3; 4}.
9. (A ∩ C) ∪ (B ∩ C) = {3; 4; 12} ∪ {3; 4} = {3; 4; 12}.
10. (A ∪ C) ∩ (B ∪ C) = {1; 3; 4; 12; 15; 27}.