2. 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 Nia
anak yang disimbolkan dengan 𝐴, dengan himpunan alat tulis, yang disombalkan
membeli pensil dan penggaris. Perhatikan bahwa ada hubungan antara himpunan
dengan 𝐵. Sehingga 𝐴 = {Tino, Ayu, Togar, Nia} dan 𝐵 = {buku tulis, pensil,
penggaris, penghapus, bolpoin, tempat pensil}. Himpunan anak dengan himpunan
alat tulis dihubungkan oleh kata membeli. Dalam hal ini, kata membeli merupakan
relasi 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 ................................................................ 41
1. Jakarta ............................... DKI Jakarta
Surabaya ........................... Jawa Timur
Semarang ........................ Jawa Tengah
Bandung ............................. Jawa Barat
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3. 2. Aceh ............................. Sumatra
Banten ................................ Jawa
Samarinda ................ Kalimantan
Manado ........................ Sulawesi
Denpasar .............................. Bali
3. Gula ............................................ manis
Garam ............................................ asin
Cabai .......................................... pedas
Merica ........................................ pedas
4. 3 ................................................ 9
1 ................................................ 3
5 .............................................. 15
0 ................................................ 0
12 ............................................ 36
5. 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.
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4. 1. 𝐴 = {… … … … … … … … … … … … … }, 𝐵 = {… … … … … … … … … … }
2. ……………………………………………………………………….
3. ……………………………………………………………………….
4. ……………………………………………………………………….
5. ……………………………………………………………………….
Dari contoh-contoh relasi di atas, diskusikan bersama dengan teman
kelompokmu untuk membahas pengertian relasi.
Relasi adalah ............................................................................................
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5. 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.
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6. 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.
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7. 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.
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