Relation www.ajwmathematics.wordpress.com

Peta Konsep www.ajwmathematics.wordpress.com

Tujuan Pembelajaran Siswa dapat menyebutkan definisi relasi Siswa dapat menyajikan relasi dalam diagram panah, himpunan pasangan berurutan, dan diagram Cartesius www.ajwmathematics.wordpress.com

Mr. Budi has five children, Riska, Dimas, Candra, Dira, and Reni Mr. Budi has five children, Riska, Dimas, Candra, Dira, and Reni. Each of them has different favorite sport. Riska likes badminton and swimming, Dimas and Candra like playing soccer, while Dira and Reni like basket and badminton. www.ajwmathematics.wordpress.com

A B www.ajwmathematics.wordpress.com According from a case, If Mr’ Budi’s children can be grouped into a set A, then element of set A are Riska, Dimas, Candra, Dira, dan Reni. We can write A = {Riska, Dimas, Candra, Dira, Reni}. While their favorite sports can be grouped into set B. We can write B = {Badminton, Swimming, Basket, Soccer} A B Riska Dimas Candra Dira Reni Badminton Swimming Basket Soccer www.ajwmathematics.wordpress.com

A B Then it can be notated into: Based from that case, the relation of them is “Favorite sports”. Riska likes badminton and swimming Dimas likes soccer Candra likes soccer Dira likes badminton and basket Reni likes badminton and basket A B Riska Dimas Candra Dira Reni Badminton Swimming Basket Soccer Both element of set A and element of set B have a relation which is favorite sports. This relation can be called as relation from set A to set B and also can be notated into Arrow Diagram Relation from set A to set B is The rule which connect elements of set A with elements of set B

Defining a Relation Between Two Sets with Cartesius Diagram Elements of set A can be put on horizontal line or x-axis. While elements of set B can be put on vertical line or y-axis. Every element of set A which has a relation with element of set B can be notated with (•) or (*). So Cartesius Diagram of previous relation can be seen below : www.ajwmathematics.wordpress.com

Menyatakan Relasi dua Himpunan dengan Pasangan Berurutan Pasangan berurutan dilambangkan dengan (x, y) dengan x menyatakan anggota suatu himpunan tertentu, sebut A, dan y menyatakan anggota dari himpunan lain, sebut B. Pada relasi gemar berolahraga sebelumnya, didapat himpunan penggemar olah raga A = {Riska, Dimas, Candra, Dira, Reni}, dan himpunan cabang olah raga B = {Badminton, Renang, Basket, Sepakbola}. Berdasarkan diagram panah sebelumnya, relasi gemar berolahraga dituliskan sebagai R = {(Riska, Renang), (Riska, Badminton), (Dimas, Sepak Bola), (Candra, Sepak Bola), (Dira, Badminton) , (Dira, Basket), (Reni, Badminton), (Reni, Basket)}. “Relasi antara himpunan X dan Y dapat dinyatakan sebagai himpunan pasangan berurutan (x, y) dengan x anggota himpunan pertama (X) dan y anggota himpunan kedua (Y).”