S = {0, 1, 2, 3, …., 16}

• A = {Faktor dari 12}
• B = {Bilangan ganjil}
• C = {Bilangan prima}
• D = {2, 4, 6, 7, 9, 13, 15}

Tentukan:

1. (A U B) ∩ (B U C) ∩ (C U D)
2. (A U B U C)ˁ ∩ (B U D)
3. S – (A U D)
4. (A U C) – (B U C)
5. (A U B)ˁ – (C U D)ˁ

Jawaban dari operasi pada himpunan tersebut adalah:

1. {2, 3, 5, 7, 9, 11, 13, 15}
2. { }
3. {0, 5, 8, 10, 11, 14, 16}
4. {4, 6, 12}
5. {0}

Penjelasan dengan langkah-langkah

Diketahui

S = {0, 1, 2, 3, …., 16}

• A = {Faktor dari 12} = {1, 2, 3, 4, 6, 12}
• B = {Bilangan ganjil} = {1, 3, 5, 7, 9, 11, 13, 15}
• C = {Bilangan prima} = {2, 3, 5, 7, 11, 13}
• D = {2, 4, 6, 7, 9, 13, 15}

Ditanyakan

1. (A U B) ∩ (B U C) ∩ (C U D)
2. (A U B U C)ˁ ∩ (B U D)
3. S – (A U D)
4. (A U C) – (B U C)
5. (A U B)ˁ – (C U D)ˁ

Jawab

Nomor 1

A U B = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15}

B U C = {1, 2, 3, 5, 7, 9, 11, 13, 15}

C U D = {2, 3, 4, 5, 6, 7, 9, 11, 13, 15}

Jadi

• (A U B) ∩ (B U C) ∩ (C U D) = {2, 3, 5, 7, 9, 11, 13, 15}

Nomor 2

(A U B U C)ˁ = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15}ˁ

                     = {0, 8, 10, 14, 16}

B U D = {1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15}

Jadi

• (A U B U C)ˁ ∩ (B U D) = { }

Nomor 3

S = {0, 1, 2, 3, 4, …., 16}

A U D = {1, 2, 3, 4, 6, 7, 9, 12, 13, 15}

Jadi

• S – (A U D) = {0, 5, 8, 10, 11, 14, 16}

Nomor 4

A U C = {1, 2, 3, 4, 5, 6, 7, 11, 12, 13}

B U C = {1, 2, 3, 5, 7, 9, 11, 13, 15}

Jadi

• (A U C) – (B U C) = {4, 6, 12}

Nomor 5

(A U B)ˁ = {1, 2, 3, 4, 5, 6, 7, 9, 11, 12, 13, 15}ˁ

              = {0, 8, 10, 14, 16}

(C U D)ˁ = {2, 3, 4, 5, 6, 7, 9, 11, 13, 15}ˁ

              = {1, 8, 10, 12, 14, 16}

Jadi

• (A U B)ˁ – (C U D)ˁ = {0}

Pelajari lebih lanjut  

Materi tentang himpunan dalam diagram venn yomemimo.com/tugas/2025298

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