Diketahui
S = {x | x ≤ 12, x bilangan cacah}
A = {bilamgan ganjil kurang dari 12}
B = {1, 2, 4, 5, 9, 11, 12}

Disajikan beberapa pernyataan berikut:
(1)   A ∪ B = {1, 2, 3, 4, 5, 7, 9, 11, 12}
(2)  B − A = {1, 2, 4, 12}
(3)  A ∩ B = {1, 5, 9, 11}
(4)  Komplemen A ∪ B = {6, 8, 10 , 11}

Pernyataan yang benar adalah … 
A.   (1) dan (3) 
B.   (1) dan (4) 
C.  (2) dan (3) 
D.  (2) dan (4) 

Jawab: A.

Himpunan S, A, dan B

  • S = {x | x ≤ 12, x bilangan cacah}
    S = {0, 1, 2, 3, 4, 5, 6, 7, 8 ,9, 10, 11, 12}

  • A = {bilamgan ganjil kurang dari 12}
    A = {1, 3, 5, 7, 9, 11}

  • B = {1, 2, 4, 5, 9, 11, 12}

Operasi gabungan dua himpunan (A ∪ B):
A = {1, 3, 5, 7, 9, 11}
B = {1, 2, 4, 5, 9, 11, 12}
A ∪ B = {1, 2, 3, 4, 5, 7, 9, 11, 12}

Selisih himpunan:
A = {1, 3, 5, 7, 9, 11}
B = {1, 2, 4, 5, 9, 11, 12}
B − A = B ∩ AC = {2, 4, 12}

Irisan dua himpunan:
A = {1, 3, 5, 7, 9, 11}
B = {1, 2, 4, 5, 9, 11, 12}
A ∩ B = {1, 5, 9, 11}

Komplemen A ∪ B :
S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A ∪ B = {1, 2, 3, 4, 5, 7, 9, 11, 12}
(A ∪ B)C = {0, 6, 8 , 10}

Sehingga,

(1) A ∪ B = {1, 2, 3, 4, 5, 7, 9, 11, 12} → BENAR
(2) B − A = {1, 2, 4, 12} → SALAH, seharusnya B − A = {2, 4, 12}
(3) A ∩ B = {1, 5, 9, 11} → BENAR
(4)  Komplemen A ∪ B = {6, 8, 10 , 11} → SALAH seharusnya A ∩ B = {1, 5, 9, 11}


Jadi, pernyataan yang benar adalah (1) dan (3).

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