AC adalah komplemen A terhadap U, jika U = {1, 2, 3, … , 9}, A = {1, 2, 3, 4} dan B = {3, 4, 5, 6}, maka (A ∩ B)C adalah …
(A) {A}
(B) {3, 4}
(C) {1, 2, 5, 6}
(D) {1, 2, 3, 4, 5, 6}
(E) {1, 2, 5, 6, 7, 8, 9}

Jawab: (E)

  • Dari soal diketahui:
    • U = {1, 2, 3, … , 9}
    • A = {1, 2, 3, 4}
    • B = {3, 4, 5, 6}
  • A ∩ B = operasi irisan dua himpunan yang menghasilkan anggota himpunan A dan B yang sama
    • A = {1, 2, 3, 4}
    • B = {3, 4, 5, 6}
    • A ∩ B = {3, 4}
  • (A ∩ B)C = himpunan anggota semesta U yang bukan merupakan himpunan aggota (A ∩ B)
    (A ∩ B)C = {1, 2, 3, 4, 5, 6, 7, 8 , 9}
    (A ∩ B)C = {1, 2, 5, 6, 7, 8 , 9}

Jadi, untuk U = {1, 2, 3, … , 9}, A = {1, 2, 3, 4} dan B = {3, 4, 5, 6}, maka (A ∩ B)c adalah {1, 2, 5, 6, 7, 8, 9} (E).

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