[Kunci Jawaban] Diketahui A = {x | x > 5, x bilangan asli}, B = {x | 3 < x < 8, x bilangan asli}, dan C = {x | 5 < x < 10, x bilangan asli}. Dengan cara mendaftar anggotanya, tentukan:

Pertanyaan:

5. Diketahui A = {x | x > 5, x bilangan asli}, B = {x | 3 < x < 8, x bilangan asli}, dan C = {x | 5 < x < 10, x bilangan asli}. Dengan cara mendaftar anggotanya, tentukan:
a. (A ∩ B) ∪ (B ∩ C)
b. (A ∪ C) ∩ (A ∪ B)

(Soal No. 5 Essay Bab Himpunan BSE Kurikulum 2013 (Revisi 2016) Semester 1 Kelas 7, Kemendikbud)
*Mungkin seharusnya A = {x | x < 5, x bilangan asli}. Tapi di sini kita mengerjakan saja apa yang tercantum di soal.

Jawaban:
Diketahui:
A = {x | x > 5, x bilangan asli}
A = {6, 7, 8, 9, 10, ...}

B = {x | 3 < x < 8, x bilangan asli}
B = {4, 5, 6, 7}

C = {x | 5 < x < 10, x bilangan asli}
C = {6, 7, 8, 9}

Ditanya:
a. (A ∩ B) ∪ (B ∩ C)
b. (A ∪ C) ∩ (A ∪ B)

Dijawab:
a. (A ∩ B) ∪ (B ∩ C)
A ∩ B = {6, 7}
B ∩ C = {6, 7}
(A ∩ B) ∪ (B ∩ C) = {6, 7}

b. (A ∪ C) ∩ (A ∪ B)
A ∪ C = {6, 7, 8, 9, 10, ...}
A ∪ B = {4, 5, 6, 7, 8, ...}
(A ∪ C) ∩ (A ∪ B) = {4, 5, 6, 7, 8, 9, ...}

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