Diberikan himpunan sebagai berikut : S = Himpunan bilangan asli yang kurang dari 16 A = Himpunan bilangan asli ganjil yang kurang dari 10 B = Himpunan bilangan prima yang kurang dari 15 Tentukan hasil operasi dari : 1. 2. 3. An B Ans Bns 4. AUB 5. A-B 6. B-A 7. 8. 9. Ac Be (An B)c 10. (AUB) 11. (A - B) 12. (B-A)
Jawab:
Penjelasan dengan langkah-langkah:
S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }
A = { 1, 3, 5, 7, 9 }
B = { 2, 3, 5, 7, 11, 13 }
1. A∩B = {3, 5, 7}
2. A∩S = {1, 3, 5, 7, 9}
3. B∩S = {2, 3, 5, 7, 11, 13}
4. A∪B = {1, 2, 3, 5, 7, 9, 11, 13}
5. A-B = {1, 9}
6. B-A = {2, 11, 13}
7. Ac = { 2, 4, 6, 8, 10, 11, 12, 13, 14, 15 }
8. Bc = { 1, 4, 6, 8, 9, 10, 12, 14, 15 }
9. A∩B = {3, 5, 7}
(A∩B)c = { 1, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15 }
10. A∪B = {1, 2, 3, 5, 7, 9, 11, 13}
(A∪B)c = { 4, 6, 8, 10, 12, 14, 15 }
11. (A-B)c = { 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15 }
12. (B-A)c = { 1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15 }
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