Himpunan-himpunan berikut :

a. Gambar diagram venn himpunan-himpunan terdapat pada lampiran.

b. (C ∩ B) - (A ⊕ C) = {2, 6, 13}

c. (A - B) ⊕ (C ∩ B) = {1, 2, 3, 6, 8, 11, 13, 15, 18, 20}

d. (C - A)⁽ ∪ (C ⊕ B) = {1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

e. (A ⊕ C) ∩ ((B - C) ⊕ A⁽ ) = {3, 5, 7, 8, 9, 10, 12, 17}

Penjelasan dengan langkah-langkah

Diketahui :

S = {x | x ≤ 20, x bilangan asli}

A = {1, 2, 5, 6, 7, 11, 12, 13, 15, 18.20}

B = { 2, 3, 4, 5. 6. 7. 8, 12, 13}

C = {1, 2, 3, 6, 8, 9, 10, 13, 17, 18}

Ditanya :

a. Gambar diagram venn himpunan-himpunan.

b. (C ∩ B) - (A ⊕ C)

c. (A - B) ⊕ (C ∩ B)

d. (C - A)⁽ ∪ (C ⊕ B)

e. (A ⊕ C) ∩ ((B - C) ⊕ A⁽ )

Jawab :

Beda setangkup dari himpunan A dan B adalah suatu himpunan yang anggotanya ada pada himpunan A atau B tapi tidak irisan keduanya yang dinotasikan :

A ⊕ B = (A ∪ B) - (A ∩ B) = (A - B) ∪ (B - A)

• a. Gambar diagram venn

Untuk gambar diagram venn himpunan-himpunan bisa dilihat pada lampiran.

• b. (C ∩ B) - (A ⊕ C)

(C ∩ B) - (A ⊕ C)

= {2, 3, 6, 8, 13} - {5, 7, 11, 12, 15,20, 3, 8, 9, 10, 17}

= {2, 6, 13}

• c. (A - B) ⊕ (C ∩ B)

(A - B) ⊕ (C ∩ B)

= {1, 11, 15, 18, 20} ⊕ {2, 3, 6, 8, 13}

= {1, 2, 3, 6, 8, 11, 13, 15, 18, 20}

• d. (C - A)⁽ ∪ (C ⊕ B)

(C - A)⁽ ∪ (C ⊕ B)

= {1, 2, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 18, 19, 20} ∪ {1, 9, 10, 17, 18, 4, 5, 7, 12}

= {1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

• e. (A ⊕ C) ∩ ((B - C) ⊕ A⁽ )

(A ⊕ C) = {3, 8, 9, 10, 17, 5, 7, 11, 12, 15, 20}

(B - C) = {4, 5, 7, 12}  

A⁽ = {3, 4, 8, 9, 10, 14, 16, 17}

(A ⊕ C) ∩ ((B - C) ⊕ A⁽ )

= {3, 8, 9, 10, 17, 5, 7, 11, 12, 15, 20} ∩ {3, 5, 7, 8, 9, 10, 12, 14, 16, 17}

= {3, 5, 7, 8, 9, 10, 12, 17}  

Pelajari lebih lanjut

Materi tentang Himpunan pada yomemimo.com/tugas/12307211

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