Roboguru

Diketahui himpunan dan himpunan . Banyak anggota adalah...

Pertanyaan

Diketahui himpunan begin mathsize 14px style K equals open curly brackets 1 comma 2 comma 3 comma 4 comma 5 close curly brackets end style dan himpunan begin mathsize 14px style L equals open curly brackets 6 comma 7 comma 8 close curly brackets end style. Banyak anggota begin mathsize 14px style K cross times L end style adalah...

  1. 5

  2. 8

  3. 15

  4. 24

  5. 27

Pembahasan Soal:

Jika A dan B adalah sembarang himpunan maka perkalian kartesian (begin mathsize 14px style A cross times B end style) dari himpunan A dan B adalah himpunan yang elemennya semua pasangan terurut (ordered pairs) yang mungkin terbentuk dengan komponen pertama dari himpunan A dan komponen kedua dari himpunan B.

Diketahui himpunan begin mathsize 14px style K equals open curly brackets 1 comma 2 comma 3 comma 4 comma 5 close curly brackets end style dan himpunan begin mathsize 14px style L equals open curly brackets 6 comma 7 comma 8 close curly brackets end style. Maka

begin mathsize 14px style K cross times L equals left curly bracket open parentheses 1 comma 6 close parentheses comma open parentheses 1 comma 7 close parentheses comma open parentheses 1 comma 8 close parentheses comma open parentheses 2 comma 6 close parentheses comma open parentheses 2 comma 7 close parentheses comma open parentheses 2 comma 8 close parentheses comma open parentheses 3 comma 6 close parentheses comma space space space space space space space space space space space space space space space open parentheses 3 comma 7 close parentheses comma open parentheses 3 comma 8 close parentheses comma open parentheses 4 comma 6 close parentheses comma open parentheses 4 comma 7 close parentheses comma open parentheses 4 comma 8 close parentheses open parentheses 5 comma 6 close parentheses comma open parentheses 5 comma 7 close parentheses comma open parentheses 5 comma 8 close parentheses right curly bracket end style

Banyak anggota begin mathsize 14px style K cross times L end style adalah 15. Jadi, jawaban yang tepat adalah C.

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 29 Maret 2021

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Pertanyaan yang serupa

Diketahui , . dan . Tentukan: b.

Pembahasan Soal:

Pertama kita tentukan S cross times M dengan menggunakan tabel:

Sehingga, S cross times M:

table attributes columnalign right center left columnspacing 0px end attributes row cell S cross times M end cell equals cell left curly bracket open parentheses straight a comma 1 close parentheses comma open parentheses straight a comma 2 close parentheses comma open parentheses straight a comma 3 close parentheses comma open parentheses straight a comma 4 close parentheses comma open parentheses straight a comma 5 close parentheses comma space end cell row blank blank cell open parentheses straight b comma 1 close parentheses comma open parentheses straight b comma 2 close parentheses open parentheses straight b comma 3 close parentheses comma open parentheses straight b comma 4 close parentheses comma open parentheses straight b comma 5 close parentheses right curly bracket end cell end table 

Kemudian kita tentukan S cross times A dengan menggunakan tabel:

Sehingga, S cross times A:

table attributes columnalign right center left columnspacing 0px end attributes row cell S cross times M end cell equals cell left curly bracket open parentheses straight a comma 3 close parentheses comma open parentheses straight a comma 5 close parentheses comma open parentheses straight a comma 7 close parentheses comma open parentheses straight a comma 9 close parentheses comma open parentheses straight b comma 3 close parentheses comma open parentheses straight b comma 5 close parentheses open parentheses straight b comma 7 close parentheses comma open parentheses straight b comma 9 close parentheses right curly bracket end cell end table

Maka,

open parentheses S cross times M close parentheses intersection open parentheses S cross times A close parentheses equals open curly brackets open parentheses a comma 3 close parentheses comma open parentheses a comma 5 close parentheses comma open parentheses b comma 3 close parentheses comma open parentheses b comma 5 close parentheses close curly brackets

Jadi, open parentheses S cross times M close parentheses intersection open parentheses S cross times A close parentheses adalah open curly brackets open parentheses a comma 3 close parentheses comma open parentheses a comma 5 close parentheses comma open parentheses b comma 3 close parentheses comma open parentheses b comma 5 close parentheses close curly brackets

0

Roboguru

Diketahui , . dan . Tentukan: a.

Pembahasan Soal:

Pertama kita tentukan S cross times M dengan menggunakan tabel:

Sehingga, S cross times M:

table attributes columnalign right center left columnspacing 0px end attributes row cell S cross times M end cell equals cell left curly bracket open parentheses straight a comma 1 close parentheses comma open parentheses straight a comma 2 close parentheses comma open parentheses straight a comma 3 close parentheses comma open parentheses straight a comma 4 close parentheses comma open parentheses straight a comma 5 close parentheses comma space end cell row blank blank cell open parentheses straight b comma 1 close parentheses comma open parentheses straight b comma 2 close parentheses open parentheses straight b comma 3 close parentheses comma open parentheses straight b comma 4 close parentheses comma open parentheses straight b comma 5 close parentheses right curly bracket end cell end table 

Kemudian kita tentukan S cross times M cross times A dengan menggunakan tabel:

Jadi,

table attributes columnalign right center left columnspacing 0px end attributes row cell S cross times M cross times A end cell equals cell left curly bracket open parentheses straight a comma 1 comma 3 close parentheses comma open parentheses straight a comma 2 comma 3 close parentheses comma open parentheses straight a comma 3 comma 3 close parentheses comma open parentheses straight a comma 4 comma 3 close parentheses comma open parentheses straight a comma 5 comma 3 close parentheses comma end cell row blank blank cell open parentheses straight b comma 1 comma 3 close parentheses comma open parentheses straight b comma 2 comma 3 close parentheses open parentheses straight b comma 3 comma 3 close parentheses comma open parentheses straight b comma 4 comma 3 close parentheses comma open parentheses straight b comma 5 comma 3 close parentheses comma space open parentheses straight a comma 1 comma 5 close parentheses comma open parentheses straight a comma 2 comma 5 close parentheses comma open parentheses straight a comma 3 comma 5 close parentheses comma open parentheses straight a comma 4 comma 5 close parentheses comma open parentheses straight a comma 5 comma 5 close parentheses comma end cell row blank blank cell open parentheses straight b comma 3 comma 5 close parentheses comma open parentheses straight b comma 4 comma 5 close parentheses comma open parentheses straight b comma 5 comma 5 close parentheses space open parentheses straight a comma 1 comma 7 close parentheses comma open parentheses straight a comma 2 comma 7 close parentheses comma open parentheses straight a comma 3 comma 7 close parentheses comma open parentheses straight a comma 4 comma 7 close parentheses comma open parentheses straight a comma 5 comma 7 close parentheses comma open parentheses straight b comma 1 comma 7 close parentheses comma open parentheses straight b comma 2 comma 7 close parentheses comma end cell row blank blank cell open parentheses straight b comma 3 comma 7 close parentheses comma open parentheses straight b comma 4 comma 7 close parentheses comma open parentheses straight b comma 5 comma 7 close parentheses comma open parentheses straight a comma 1 comma 9 close parentheses comma open parentheses straight a comma 2 comma 9 close parentheses comma end cell row blank blank cell open parentheses straight a comma 3 comma 9 close parentheses comma open parentheses straight a comma 4 comma 9 close parentheses comma open parentheses straight a comma 5 comma 9 close parentheses comma open parentheses straight b comma 1 comma 9 close parentheses comma open parentheses straight b comma 2 comma 9 close parentheses comma end cell row blank blank cell open parentheses straight b comma 3 comma 9 close parentheses comma open parentheses straight b comma 4 comma 9 close parentheses comma open parentheses straight b comma 5 comma 9 close parentheses right curly bracket end cell end table 

 

0

Roboguru

Diketahui , , dan . Tentukan: b. .

Pembahasan Soal:

Pertama kita tentukan A cross times B dengan menggunakan tabel:

Sehingga, A cross times B :

straight A cross times straight B equals open curly brackets open parentheses straight a comma straight b close parentheses comma open parentheses straight a comma straight c close parentheses comma open parentheses straight a comma straight d close parentheses comma open parentheses straight b comma straight b close parentheses comma open parentheses straight b comma straight c close parentheses open parentheses straight b comma straight d close parentheses comma open parentheses straight c comma straight b close parentheses comma open parentheses straight c comma straight c close parentheses comma open parentheses straight c comma straight d close parentheses close curly brackets

Kemudian kita tentukan A cross times B cross times C  dengan menggunakan tabel:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight A cross times straight B cross times straight C end cell equals cell left curly bracket open parentheses straight a comma straight b comma straight a close parentheses comma open parentheses straight a comma straight c comma straight a close parentheses comma open parentheses straight a comma straight d comma straight a close parentheses comma open parentheses straight b comma straight b comma straight a close parentheses comma open parentheses straight b comma straight c comma straight a close parentheses open parentheses straight b comma straight d comma straight a close parentheses comma end cell row blank blank cell open parentheses straight c comma straight b comma straight a close parentheses comma open parentheses straight c comma straight c comma straight a close parentheses comma open parentheses straight c comma straight d comma straight a close parentheses open parentheses straight a comma straight b comma straight d close parentheses comma open parentheses straight a comma straight c comma straight d close parentheses comma open parentheses straight a comma straight d comma straight d close parentheses comma end cell row blank blank cell open parentheses straight b comma straight b comma straight d close parentheses comma open parentheses straight b comma straight c comma straight d close parentheses open parentheses straight b comma straight d comma straight d close parentheses comma open parentheses straight c comma straight b comma straight d close parentheses comma open parentheses straight c comma straight c comma straight d close parentheses comma open parentheses straight c comma straight d comma straight d close parentheses right curly bracket end cell end table 

Sehingga, n open parentheses A cross times B cross times C close parentheses equals 18

Jadi, n open parentheses A cross times B cross times C close parentheses adalah 18

 

0

Roboguru

Diketahui A= {a, b, c}, B = {b, c, d}, dan C = {a, d}. Tentukan: a. .

Pembahasan Soal:

Pertama kita tentukan A cross times B dengan menggunakan tabel:

Sehingga, A cross times B :

straight A cross times straight B equals open curly brackets open parentheses straight a comma straight b close parentheses comma open parentheses straight a comma straight c close parentheses comma open parentheses straight a comma straight d close parentheses comma open parentheses straight b comma straight b close parentheses comma open parentheses straight b comma straight c close parentheses open parentheses straight b comma straight d close parentheses comma open parentheses straight c comma straight b close parentheses comma open parentheses straight c comma straight c close parentheses comma open parentheses straight c comma straight d close parentheses close curly brackets

Kemudian kita tentukan A cross times B cross times C  dengan menggunakan tabel:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight A cross times straight B cross times straight C end cell equals cell left curly bracket open parentheses straight a comma straight b comma straight a close parentheses comma open parentheses straight a comma straight c comma straight a close parentheses comma open parentheses straight a comma straight d comma straight a close parentheses comma open parentheses straight b comma straight b comma straight a close parentheses comma open parentheses straight b comma straight c comma straight a close parentheses open parentheses straight b comma straight d comma straight a close parentheses comma end cell row blank blank cell open parentheses straight c comma straight b comma straight a close parentheses comma open parentheses straight c comma straight c comma straight a close parentheses comma open parentheses straight c comma straight d comma straight a close parentheses open parentheses straight a comma straight b comma straight d close parentheses comma open parentheses straight a comma straight c comma straight d close parentheses comma open parentheses straight a comma straight d comma straight d close parentheses comma end cell row blank blank cell open parentheses straight b comma straight b comma straight d close parentheses comma open parentheses straight b comma straight c comma straight d close parentheses open parentheses straight b comma straight d comma straight d close parentheses comma open parentheses straight c comma straight b comma straight d close parentheses comma open parentheses straight c comma straight c comma straight d close parentheses comma open parentheses straight c comma straight d comma straight d close parentheses right curly bracket end cell end table 

 

0

Roboguru

Sketch, by shading the appropriate area, each of the following product sets on coordinate Cartesian diagram of . c.

Pembahasan Soal:

Diketahui, bahwa daerah asal dari perkalian himpunanan di atas yaitu D subscript f equals left square bracket negative 3 comma 1 right parenthesis sedangkan kodomainnya K subscript f equals left parenthesis negative infinity comma 2 right square bracket , sehiingga pada koordinat kartesius dapat digambarkan:

0

Roboguru

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