LKS: Pengertian Relasi

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LKS: Pengertian Relasi

  1. 1. A. Pengertian Relasi Tino, Ayu, Togar, dan Nia berada di sebuah toko alat tulis. Mereka berencana membeli buku dan alat tulis. Tino berencana membeli buku tulis dan pensil, Ayu membeli penggaris dan penghapus, Togar membeli bolpoin, buku tulis, dan tempat pensil, sedangkan Niaanak yang disimbolkan dengan 𝐴, dengan himpunan alat tulis, yang disombalkanmembeli pensil dan penggaris. Perhatikan bahwa ada hubungan antara himpunandengan 𝐵. Sehingga 𝐴 = {Tino, Ayu, Togar, Nia} dan 𝐵 = {buku tulis, pensil,penggaris, penghapus, bolpoin, tempat pensil}. Himpunan anak dengan himpunanalat tulis dihubungkan oleh kata membeli. Dalam hal ini, kata membeli merupakanrelasi yang menghubungkan himpunan anak dengan himpunan alat tulis.Isilah titik-titik di bawah ini agar pernyataan-pernyataan berikut bernilai benar! Contoh: 3 lebihnya dari 14 ................................................................ 11 3 lebihnya dari 3 .................................................................... 0 3 lebihnya dari 23 ................................................................ 20 3 lebihnya dari 44 ................................................................ 411. Jakarta ............................... DKI Jakarta Surabaya ........................... Jawa Timur Semarang ........................ Jawa Tengah Bandung ............................. Jawa Baratyos3prens.wordpress.com 1
  2. 2. 2. Aceh ............................. Sumatra Banten ................................ Jawa Samarinda ................ Kalimantan Manado ........................ Sulawesi Denpasar .............................. Bali3. Gula ............................................ manis Garam ............................................ asin Cabai .......................................... pedas Merica ........................................ pedas 4. 3 ................................................ 9 1 ................................................ 3 5 .............................................. 15 0 ................................................ 0 12 ............................................ 365. 4 ....................................................... 11 7 ....................................................... 14 15 ..................................................... 22 57 ..................................................... 64 Perhatikan contoh di atas. “Tiga lebihnya dari” adalah relasi antara himpunan bilangan-bilangan di sisi kiri dengan kanan. Sekarang relasi apa yang kalian isikan pada nomor 1 – 5? 1. ……………………………………… 2. ……………………………………… 3. ……………………………………… 4. ……………………………………… 5. ……………………………………… Relasi-relasi di atas menghubungkan himpunan di sisi kiri dengan himpunan di sisi kanan. Pada contoh di atas, dimisalkan himpunan bilangan-bilangan di maka 𝐴 = {14, 3, 23, 44}, 𝐵 = {11, 0, 20, 41}. Sekarang daftarlah himpunan- sisi kiri adalah A dan himpunan bilangan-bilangan di sisi kanan adalah B, himpunan dari nomor 1 sampai 5.yos3prens.wordpress.com 2
  3. 3. 1. 𝐴 = {… … … … … … … … … … … … … }, 𝐵 = {… … … … … … … … … … } 2. ………………………………………………………………………. 3. ………………………………………………………………………. 4. ………………………………………………………………………. 5. ………………………………………………………………………. Dari contoh-contoh relasi di atas, diskusikan bersama dengan teman kelompokmu untuk membahas pengertian relasi. Relasi adalah ............................................................................................ ............................................................................................................................. ............................................................................................................................. .............................................................................................................................yos3prens.wordpress.com 3
  4. 4. B. Menyatakan Relasi Dua Himpunan dengan Diagram Panah Relasi pada contoh di atas dapat dinyatakan dengan diagram panah, yaitu: 3 lebihnya dari 𝑨 𝑩 14 11 3 0 23 20 44 41 Sekarang nyatakan soal nomor 1 – 5 di atas dengan diagram panah. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. 4 .............................................................................................................................yos3prens.wordpress.com
  5. 5. C. Menyatakan Relasi Dua Himpunan dalam Koordinat Cartesius Relasi pada contoh di atas dapat dinyatakan dalam koordinat Cartesius, yaitu: 41 20 11 3 14 23 44 Sekarang nyatakan soal nomor 1 – 5 di atas dalam koordinat Cartesius. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. 5 .............................................................................................................................yos3prens.wordpress.com
  6. 6. D. Menyatakan Relasi Dua Himpunan dengan Pasangan Berurutan Relasi pada contoh di atas dapat dinyatakan dengan himpunan pasangan 𝑅 = {(3, 0), (14, 11), (23, 20), (44, 41)} berurutan, yaitu: Sekarang nyatakan soal nomor 1 – 5 di atas dengan himpunan pasangan berurutan. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. .............................................................................................................................yos3prens.wordpress.com 6

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