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Diketahui  : straight U equals open curly brackets 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets

Himpunan bagian adalah :

straight A equals open curly brackets 1 comma space 3 comma space 5 comma space 7 comma space 9 close curly brackets straight B equals open curly brackets 2 comma space 4 comma space 5 comma space 6 comma space 7 close curly brackets straight C equals open curly brackets 3 comma space 6 comma space 7 comma space 9 close curly brackets 

Tentukan elemen-elemen dalam himpunan berikut :

 open parentheses A union B close parentheses intersection open parentheses A union C close parentheses  

N. Puspita

Master Teacher

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Pembahasan

Diketahui :

straight A equals open curly brackets 1 comma space 3 comma space 5 comma space 7 comma space 9 close curly brackets straight B equals open curly brackets 2 comma space 4 comma space 5 comma space 6 comma space 7 close curly brackets straight C equals open curly brackets 3 comma space 6 comma space 7 comma space 9 close curly brackets

Untuk mengetahui open parentheses A union B close parentheses intersection open parentheses A union C close parentheses , kita harus mencari A union B, gabungan dari dua himpunan A dan B dan A union C terlebih dahulu, yaitu gabungan dari dua himpunan A dan C.

 straight A equals open curly brackets 1 comma space 3 comma space 5 comma space 7 comma space 9 close curly brackets straight B equals open curly brackets 2 comma space 4 comma space 5 comma space 6 comma space 7 close curly brackets straight C equals open curly brackets 3 comma space 6 comma space 7 comma space 9 close curly brackets  A union B equals open curly brackets 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets A union C equals open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets 

Selanjutnya kita cari open parentheses A union B close parentheses intersection open parentheses A union C close parentheses yaitu irisan dari dua himpunan A union B dan A union C :

 A union B equals open curly brackets 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets A union C equals open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets  open parentheses A union B close parentheses intersection open parentheses A union C close parentheses equals open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets 

Jadi, elemen-elemen dalam himpunan  open parentheses A union B close parentheses intersection open parentheses A union C close parentheses  adalah open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 9 close curly brackets 

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