LKS: Pengertian Relasi

yos3prens.wordpress.com

1

A. Pe nge r t ian Re l a s i

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

membeli pensil dan penggaris. Perhatikan bahwa ada hubungan antara himpunan

anak yang disimbolkan dengan 𝐴, dengan himpunan alat tulis, yang disombalkan

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:

14 ................................................................ 11

3 .................................................................... 0

23 ................................................................ 20

44 ................................................................ 41

1. Jakarta ............................... DKI Jakarta

Surabaya ........................... Jawa Timur

Semarang ........................ Jawa Tengah

Bandung ............................. Jawa Barat

3 lebihnya dari

3 lebihnya dari

3 lebihnya dari

3 lebihnya dari


2

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

sisi kiri adalah A dan himpunan bilangan-bilangan di sisi kanan adalah B,

maka 𝐴 = {14, 3, 23, 44}, 𝐵 = {11, 0, 20, 41}. Sekarang daftarlah himpunan-

himpunan dari nomor 1 sampai 5.


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 ............................................................................................

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................


4

B. M e nyat ak an Re l as i Dua H i m punan de ngan D i agr am Panah Relasi pada contoh di atas dapat dinyatakan dengan diagram panah, yaitu:

Sekarang nyatakan soal nomor 1 – 5 di atas dengan diagram panah. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. .............................................................................................................................

14

3

23

44

11

0

20

41

𝑨 𝑩

3 lebihnya dari


5

C. M e nyat ak an Re l as i Dua H i m punan da l am K oor d i nat Car t e s i us Relasi pada contoh di atas dapat dinyatakan dalam koordinat Cartesius, yaitu: Sekarang nyatakan soal nomor 1 – 5 di atas dalam koordinat Cartesius. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. .............................................................................................................................

3

41

44 23 14

20

11


6

D. M e nyat ak an Re l as i Dua H i m punan de ngan P as angan Be r ur ut an Relasi pada contoh di atas dapat dinyatakan dengan himpunan pasangan berurutan, yaitu:

𝑅 = {(3, 0), (14, 11), (23, 20), (44, 41)} Sekarang nyatakan soal nomor 1 – 5 di atas dengan himpunan pasangan berurutan. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. .............................................................................................................................

LKS: Pengertian Relasi

Education

Transcript of LKS: Pengertian Relasi