Roboguru

Diketahui   dan  Tentukan:

Pertanyaan

Diketahui S equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 right curly bracket comma P equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 right curly bracket dan Q equals left curly bracket 2 comma space 4 comma space 6 comma space 7 right curly bracket. Tentukan:

a. space left parenthesis P intersection Q right parenthesis to the power of c 

Pembahasan Soal:

Ingat kembali bahwa:

  • Irisan dua himpunan begin mathsize 14px style A end style dan size 14px B (begin mathsize 14px style A intersection B end style) adalah himpunan dari semua anggota himpunan begin mathsize 14px style A end style dan size 14px B yang memiliki anggota yang sama. 
  • Suatu komplemen himpunan begin mathsize 14px style A end style (begin mathsize 14px style A to the power of c end style) adalah himpunan yang anggotanya merupakan anggota himpunan semesta open parentheses S close parentheses tapi bukan anggota begin mathsize 14px style A end style.

Diketahui:

  • S equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 right curly bracket 
  • P equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 right curly bracket
  • Q equals left curly bracket 2 comma space 4 comma space 6 comma space 7 right curly bracket

Ditanya:

  • left parenthesis P intersection Q right parenthesis to the power of c space ?

Penyelesaian:

Langkah pertama: Tentukan himpunan P intersection Q terlebih dahulu. 

table attributes columnalign right center left columnspacing 0px end attributes row cell P intersection Q end cell equals cell left curly bracket up diagonal strike 1 comma space 2 comma space up diagonal strike 3 comma space 4 comma space up diagonal strike 5 right curly bracket space intersection space left curly bracket 2 comma space 4 comma up diagonal strike space 6 end strike comma space up diagonal strike 7 right curly bracket end cell row cell P intersection Q end cell equals cell open curly brackets 2 comma space 4 close curly brackets end cell end table

Sehingga, himpunan dari P intersection Q adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 2 comma space 4 close curly brackets end cell end table.

Langkah kedua: Tentukan himpunan left parenthesis P intersection Q right parenthesis to the power of c dengan menggunakan P intersection Q dan himpunan semesta open parentheses S close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis P intersection Q right parenthesis to the power of c end cell equals cell open parentheses P intersection Q close parentheses space intersection space open parentheses S close parentheses end cell row blank equals cell open curly brackets up diagonal strike 2 comma space up diagonal strike 4 close curly brackets space intersection space left curly bracket 1 comma up diagonal strike space 2 end strike comma space 3 comma up diagonal strike space 4 end strike comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 right curly bracket end cell row cell left parenthesis P intersection Q right parenthesis to the power of c end cell equals cell left curly bracket 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 right curly bracket end cell end table

Dengan demikian, himpunan left parenthesis P intersection Q right parenthesis to the power of c pada soal tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left curly bracket 1 comma space 3 comma space 5 comma space 6 comma space 7 comma space 8 comma space 9 comma space 10 right curly bracket end cell end table.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

L. Sibuea

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 12 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Jika , , dan .  Tentukan hasil dari .

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x minus 1 close parentheses squared end cell equals 0 row x equals 1 row E equals cell left curly bracket 1 right curly bracket end cell row blank blank blank row cell x squared end cell equals 1 row x equals 1 row F equals cell left curly bracket 1 right curly bracket end cell row blank blank blank row cell x squared minus 3 x plus 2 end cell equals 0 row cell left parenthesis x minus 2 right parenthesis left parenthesis x minus 1 right parenthesis end cell equals 0 row cell x subscript 1 end cell equals cell 2 space space x subscript 2 equals 1 end cell row G equals cell left curly bracket 1 comma space 2 right curly bracket end cell row blank blank blank row blank blank blank row blank blank blank end table end style

Asumsikan begin mathsize 14px style S equals left curly bracket 1 comma space 2 right curly bracket end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F to the power of C end cell equals cell left curly bracket 2 right curly bracket end cell row cell E intersection F to the power of C end cell equals cell left curly bracket 1 comma space 2 right curly bracket end cell row cell left parenthesis E intersection F to the power of C right parenthesis union G end cell equals cell left curly bracket 1 comma space 2 right curly bracket end cell end table end style

1

Roboguru

Diketahui himpunan-himpunan berikut: Dari himpunan di atas, tentukan himpunan berikut dengan mendaftar anggotanya!

Pembahasan Soal:

Pertama-tama, nyatakan himpunan A. space B. space C dengan mendaftar anggota-anggotanya sebagai berikut.

A equals open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets B equals open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 comma space 12 close curly brackets C equals open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets

Lalu selesaikan A intersection B intersection C sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell A intersection B intersection C end cell equals cell open parentheses A intersection B close parentheses intersection C end cell row blank equals cell open parentheses open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets intersection open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 comma space 12 close curly brackets close parentheses intersection open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets end cell row blank equals cell open curly brackets 2 comma space 6 comma space 10 close curly brackets intersection open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets end cell row blank equals cell open curly brackets 2 close curly brackets end cell end table

Dengan demikian, hasil dari A intersection B intersection C adalah open curly brackets 2 close curly brackets.

1

Roboguru

Diketahui himpunan-himpunan berikut: Dari himpunan di atas, tentukan himpunan berikut dengan mendaftar anggotanya!

Pembahasan Soal:

Pertama-tama, nyatakan himpunan A. space B. space C dengan mendaftar anggota-anggotanya sebagai berikut.

A equals open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets B equals open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 comma space 12 close curly brackets C equals open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets

Lalu selesaikan A intersection B union C sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell A intersection B union C end cell equals cell open parentheses A intersection B close parentheses union C end cell row blank equals cell open parentheses open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets intersection open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 comma space 12 close curly brackets close parentheses union open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets end cell row blank equals cell open curly brackets 2 comma space 6 comma space 10 close curly brackets union open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets end cell row blank equals cell open curly brackets 2 comma space 3 comma space 5 comma space 6 comma space 7 comma space 10 comma space 11 comma space 13 close curly brackets end cell end table

Dengan demikian, hasil dari A intersection B union C adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open curly brackets 2 comma space 3 comma space 5 comma space 6 comma space 7 comma space 10 comma space 11 comma space 13 close curly brackets end cell end table.

0

Roboguru

Diketahui himpunan-himpunan berikut: Dari himpunan di atas, tentukan himpunan berikut dengan mendaftar anggotanya!

Pembahasan Soal:

Pertama-tama, nyatakan himpunan A. space B. space C dengan mendaftar anggota-anggotanya sebagai berikut.

A equals open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets B equals open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 comma space 12 close curly brackets C equals open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets

Lalu selesaikan A minus open parentheses B intersection C close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell A minus open parentheses B intersection C close parentheses end cell equals cell open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets minus open parentheses open curly brackets 2 comma space 4 comma space 6 comma space 8 comma space 10 comma space 12 close curly brackets intersection open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 close curly brackets close parentheses end cell row blank equals cell open curly brackets 1 comma space 2 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets minus open curly brackets 2 close curly brackets end cell row blank equals cell open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets end cell end table

Dengan demikian, hasil dari A minus open parentheses B intersection C close parentheses adalah open curly brackets 1 comma space 3 comma space 5 comma space 6 comma space 10 comma space 15 comma space 30 close curly brackets.

1

Roboguru

Diketahui himpunan-himpunan berikut: S = , P = , dan Q = . Nyatakan himpunan-himpunan berikut dengan mendaftar anggota-anggotanya! c.   d.

Pembahasan Soal:

Terlebih dahulu dicari anggota himpunan di dalam tanda kurung kemudian dilanjutkan dengan konsep komplemen himpunan maka diperoleh:

Soal c.

open parentheses P intersection Q close parentheses equals open curly brackets 2 close curly brackets 

Anggota open parentheses P intersection Q close parentheses apostrophe adalah semua anggota S yang bukan 2. Dengan demikian, open parentheses P intersection Q close parentheses apostrophe equals open curly brackets 0 comma space 1 comma space 3 comma space 4 comma space 5 comma space 6 comma space 7 comma space 8 close curly brackets 

Soal d.

open parentheses P union Q close parentheses equals open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 1 comma space 4 comma space 8 close curly brackets 

Anggota open parentheses P union Q close parentheses apostrophe adalah semua anggota S yang bukan 2, 3, 5, 7, 1, 4 dan 8. Dengan demikian, open parentheses P union Q close parentheses apostrophe equals open curly brackets 0 comma space 6 close curly brackets.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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