{"id":304592,"date":"2021-11-01T00:00:32","date_gmt":"2021-10-31T17:00:32","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=304592"},"modified":"2023-02-07T15:38:26","modified_gmt":"2023-02-07T08:38:26","slug":"relasi-dan-fungsi","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/relasi-dan-fungsi\/","title":{"rendered":"Relasi dan Fungsi &#8211; Pengertian, Perbedaan dan Cara Menyatakannya"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"533\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Relasi-dan-Fungsi.webp\" alt=\"\" class=\"wp-image-304600\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Relasi-dan-Fungsi.webp 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Relasi-dan-Fungsi-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Relasi-dan-Fungsi-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Relasi-dan-Fungsi-263x175.webp?crop=1 263w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika ada himpunan A = {Tokyo, Bangkok, Seoul}, B = {Thailand, Korea Selatan, dan Jepang}, dan C = {kimchi, pad thai, bulgogi, sushi}, bagaimana ya hubungan antara ketiganya? Himpunan A dan B merupakan fungsi\/relasi dan himpunan B dan C adalah relasi. Ingin tahu perbedaan relasi dan fungsi? <\/span><i><span style=\"font-weight: 400;\">Check this out<\/span><\/i><span style=\"font-weight: 400;\">!<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Pengertian Relasi<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi adalah hubungan antara himpunan dari daerah asal (domain) dan daerah kawan (kodomain).&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Anggota himpunan dari daerah asal dipasangkan dengan anggota himpunan dari daerah kawan sesuai dengan relasinya. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {Tokyo, Bangkok, Seoul}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {Thailand, Korea Selatan, Jepang}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">C = {kimchi, pad thai, bulgogi, sushi}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi antara himpunan A dan B<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">R: <\/span><i><span style=\"font-weight: 400;\">A<\/span><\/i> <span style=\"font-weight: 400;\">-&gt;<\/span> <i><span style=\"font-weight: 400;\">B<\/span><\/i><span style=\"font-weight: 400;\"> = {(Tokyo, Jepang), (Bangkok, Thailand), (Seoul, Korea Selatan)}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Setiap anggota himpunan A tepat berpasangan dengan setiap satu anggota himpunan B, sehingga relasinya disebut sebagai fungsi atau lebih spesifiknya korespondensi satu-satu.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi antara himpunan C dan B<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {Thailand, Korea Selatan, Jepang}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">C = {kimchi, pad thai, bulgogi, sushi}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><i><span style=\"font-weight: 400;\">R<\/span><\/i><span style=\"font-weight: 400;\">: <\/span><i><span style=\"font-weight: 400;\">B <\/span><\/i><span style=\"font-weight: 400;\">-&gt;<\/span> <i><span style=\"font-weight: 400;\">C<\/span><\/i><span style=\"font-weight: 400;\"> = {(Thailand, pad thai), (Korea Selatan, kimchi), (Korea Selatan, bulgogi), (Jepang, sushi)}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Hubungan di atas bukanlah fungsi karena ada satu anggota himpunan B yang berpasangan dengan 2 anggota himpunan C, yaitu Korea Selatan yang berpasangan dengan kimchi dan bulgogi. Namun, keduanya masih termasuk relasi.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Contoh relasi dalam kehidupan sehari-hari juga bisa kamu lihat pada silsilah keluarga di mana setiap orangtua bisa memiliki anak lebih dari satu.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Cara Menyatakan Relasi<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi bisa dinyatakan dalam beberapa bentuk, yaitu sebagai berikut.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>1. Diagram panah<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Cara menyatakannya adalah dengan membuat dua bangun yang merepresentasikan domain dan kodomain. Di dalam bangun tersebut diberi tanda berupa titik sebanyak anggota himpunannya.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Lalu, hubungkan titik-titik dari daerah domain menuju titik-titik daerah kodomain menggunakan tanda panah. Perhatikan dua contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Contoh 1<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {1, 2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {1, 4, 9, 16, 25}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tuliskan dahulu domain serta kodomainnya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain: A = {1, 2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain: B = {1, 4, 9, 16, 25}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi: A akar dari B<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Model: <\/span><em><span style=\"font-weight: 400;\">R: \u221ax&nbsp;<\/span><\/em><span style=\"font-weight: 400;\">-&gt;<\/span> <em><span style=\"font-weight: 400;\">x<\/span><\/em><sup><span style=\"font-weight: 400;\">2<\/span><\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Bentuk diagram panahnya adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"355\" height=\"303\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-a.webp\" alt=\"\" class=\"wp-image-304608\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Daerah hasil atau biasa disebut range = {1, 4, 9, 16}. Untuk 25 tidak termasuk hasil karena tidak memiliki pasangan dari daerah domain.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Contoh 2<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">P = {2, 3, 4, 5}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Q = {4, 7, 8, 9, 10}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tuliskan dahulu domain dan kodomainnya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain: P = {2, 3, 4, 5}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain: Q = {4, 7, 8, 9, 10}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi: A faktor dari B<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"371\" height=\"278\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-b.webp\" alt=\"\" class=\"wp-image-304607\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-b.webp 371w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-b-200x150.webp?crop=1 200w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Coba Quipperian perhatikan dua contoh diagram panah di atas. Adakah perbedaan antara keduanya?<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Pada contoh 1, setiap anggota domain tepat berpasangan dengan satu anggota kodomain secara berurutan. Dengan demikian, diagram panah tersebut menunjukkan suatu relasi yang disebut <\/span><b>himpunan pasangan berurutan<\/b><span style=\"font-weight: 400;\">.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Sementara itu, pada contoh 2 satu anggota domain ada yang berpasangan dengan dua anggota kodomain. Artinya, diagram panah tersebut hanya disebut relasi.<\/span><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><b>2. Diagram Cartesius<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Selain diagram panah, relasi juga bisa ditulis dalam bentuk diagram Cartesius. Sumbu X menunjukkan daerah domain dan sumbu Ynya daerah kodomain. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {1, 2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {1, 4, 9, 16, 25}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tuliskan dahulu domain serta kodomainnya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain: A = {2, 3, 4, 5, 6}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain: B = {1, 2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Relasi: <\/span><i><span style=\"font-weight: 400;\">R<\/span><\/i><span style=\"font-weight: 400;\">: <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i> <span style=\"font-weight: 400;\">-&gt;<\/span> <i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> + 1<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Diagram Cartesisunya digambarkan seperti berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"614\" height=\"357\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-c.webp\" alt=\"\" class=\"wp-image-304606\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Pengertian Fungsi (Pemetaan)<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Fungsi adalah hubungan antara daerah domain dan kodomian, di mana setiap satu anggota domain tepat berpasangan dengan satu anggota kodomain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, fungsi merupakan bentuk relasi khusus. Setiap fungsi sudah bisa dipastikan relasi.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Namun, setiap relasi belum tentu fungsi. Adapun syarat khusus yang harus dipenuhi suatu relasi agar bisa dikatakan fungsi.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Tidak boleh ada anggota domain yang tidak berpasangan. Artinya, seluruh anggota domain harus memiliki pasangan.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Tidak boleh ada anggota domain yang berpasangan lebih dari satu atau bercabang.<\/span><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Jenis-Jenis Fungsi<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Secara umum, fungsi dibagi menjadi tiga jenis yaitu sebagai berikut.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>1. Fungsi injektif<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Fungsi injektif adalah fungsi yang anggota kodomainnya hanya boleh berpasangan dengan satu anggota domain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pada injektif ini, anggota kodomain boleh tidak berpasangan. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"284\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-d.webp\" alt=\"\" class=\"wp-image-304605\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Setiap anggota domain tepat berpasangan dengan satu anggota kodomain. Namun, masih ada anggota kodomain yang tidak berpasangan.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>2. Fungsi surjektif<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Fungsi surjektif adalah fungsi yang anggota kodomainnya tidak boleh ada yang tidak berpasangan.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pada surjektif ini, setiap anggota kodomain boleh berpasangan dengan lebih dari satu anggota domain. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"294\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-e.webp\" alt=\"\" class=\"wp-image-304604\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><b>3. Fungsi bijektif<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Adalah fungsi yang anggota kodomainnya tidak boleh ada yang tidak berpasangan dan setiap anggota kodomain harus berpasangan dengan tepat satu anggota domain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, anggota kodomain tidak boleh bercabang. Perhatikan contoh berikut. Bijektif ini biasa disebut korespondensi satu-satu.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"361\" height=\"318\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-f.webp\" alt=\"\" class=\"wp-image-304603\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Notasi Fungsi<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Penulisan fungsi sama seperti relasi, misalnya notasi dari fungsi A ke B bisa dinyatakan sebagai <\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">: A <\/span><span style=\"font-weight: 400;\">-&gt;<\/span><span style=\"font-weight: 400;\"> B, <\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">a<\/span><\/i><span style=\"font-weight: 400;\">) = <\/span><i><span style=\"font-weight: 400;\">b<\/span><\/i><span style=\"font-weight: 400;\">. Notasi tersebut memiliki arti fungsi <\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\"> memetakan setiap anggota himpunan A dengan satu anggota himpunan B.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Untuk lebih jelasnya, perhatikan contoh soal berikut.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Contoh Soal 1<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Sebuah fungsi <\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">: <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i> <span style=\"font-weight: 400;\">-&gt;<\/span> <i><span style=\"font-weight: 400;\">y<\/span><\/i><span style=\"font-weight: 400;\"> dengan&nbsp; <\/span><i><span style=\"font-weight: 400;\">f<\/span><\/i><span style=\"font-weight: 400;\">(<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">) = 4 + 2<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> memiliki daerah asal {1, 3, 5, 7}. Gambarkan diagram panah fungsi tersebut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pertama, tentukan dahulu daerah kawan (kodomain) yang anggotanya sama dengan daerah hasil. Caranya adalah dengan mensubstitusikan nilai daerah asal pada persamaan fungsi yang tersedia.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"166\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-g.webp\" alt=\"\" class=\"wp-image-304602\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\"> <\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dengan demikian, daerah hasilnya adalah {6, 10, 14, 18}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika digambarkan dalam bentuk diagram panah, menjadi seperti berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"289\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/relasi-dan-fungsi-h.webp\" alt=\"\" class=\"wp-image-304601\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Contoh Soal 2<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pak Hasan memiliki himpunan S, T, U, V, dan W yang masing-masing anggotanya adalah sebagai berikut.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">S = {(3,2), (4,3), (5,7), (6,8)}<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">T = {(2,3), (2,4), (3,5), (4,7)}<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">U = {(1,3), (2,3), (3,5),(4,9)}<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">V = {(4,5), (1,2), (3,9), (7,10)}<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">W = {(1,2), (1,3), (2,3), (2,4)}<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan jenis himpunan yang dimiliki Pak Hasan tersebut!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Himpunan S = {(3,2), (4,3), (5,7), (6,8)}<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain = {3, 4, 5, 7}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain = {2, 3, 7, 8}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diperhatikan, setiap anggota himpunan domain tepat berpasangan dengan satu anggota himpunan kodomain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tidak hanya itu, setiap satu anggota kodomain hanya memiliki satu pasang anggota domain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, himpunan S merupakan fungsi bijektif atau korespondensi satu-satu.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Himpunan T = {(2,3), (2,4), (3,5), (4,7)}<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain = {2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain = {3, 4, 5, 7}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diperhatikan, ada satu anggota domain yang berpasangan dengan dua anggota kodomain, yaitu (2,3) dan (2,4).&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, himpunan T merupakan relasi atau tidak termasuk fungsi.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Himpunan U = {(1,3), (2,3), (3,5), (4,9)}<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain = {1, 2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain = {3, 5, 9}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diperhatikan, setiap satu anggota domain berpasangan dengan tepat satu anggota kodomain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Namun, ada anggota kodomain yang berpasangan dengan dua anggota domain. Artinya, himpunan U merupakan fungsi surjektif.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Himpunan V = {(4,5), (1,2), (3,9), (7,10)}<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain = {4, 1, 3, 7}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain = {5, 2, 9, 10}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diperhatikan, setiap anggota himpunan domain tepat berpasangan dengan satu anggota himpunan kodomain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tidak hanya itu, setiap satu anggota kodomain hanya memiliki satu pasang anggota domain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, himpunan V merupakan fungsi bijektif atau korespondensi satu-satu.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Himpunan W = {(1,2), (1,3), (2,3), (2,4)}<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Domain = {1, 2}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kodomain = { 2, 3, 4}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diperhatikan, satu anggota domain berpasangan dengan lebih dari satu anggota kodomain.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, himpunan W merupakan relasi atau tidak termasuk fungsi.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, himpunan S = fungsi bijektif, himpunan T = relasi, himpunan U = fungsi surjektif, himpunan V = fungsi bijektif, dan himpunan W = relasi.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Itulah pembahasan Quipper Blog kali ini tentang relasi dan fungsi. Semoga bisa membantu Quipperian memahami Matematika dengan lebih menyenangkan, ya.&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jangan lupa gabung bersama <\/span><a href=\"https:\/\/subscribe.quipper.com\/signup\"><b>Quipper Video<\/b><\/a><span style=\"font-weight: 400;\"> supaya kamu bisa akses materi belajar di mana saja dan kapan saja. Tak hanya lewat tayangan video, kamu juga bisa belajar lewat rangkuman materi dan latihan soal. Segera daftar, ya!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Penulis: Eka Viandari<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jika ada himpunan A = {Tokyo, Bangkok, Seoul}, B = {Thailand, Korea Selatan, dan Jepang}, dan C = {kimchi, pad thai, bulgogi, sushi}, bagaimana&hellip;<\/p>\n","protected":false},"author":99400369,"featured_media":304600,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[],"ppma_author":[679386827,679386836],"class_list":["post-304592","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Relasi dan Fungsi - Pengertian, Perbedaan dan Cara Menyatakannya - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Relasi dan Fungsi matematika kelas 10, simak mulai dari pengertian, apa perbedaan relasi dan fungsi dan cara menyatakannya\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/relasi-dan-fungsi\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Relasi dan Fungsi - Pengertian, Perbedaan dan Cara Menyatakannya - Quipper Blog\" \/>\n<meta property=\"og:description\" content=\"Relasi dan Fungsi matematika kelas 10, simak mulai dari pengertian, apa perbedaan relasi dan fungsi dan cara menyatakannya\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/relasi-dan-fungsi\/\" \/>\n<meta property=\"og:site_name\" content=\"Quipper Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/QuipperVideoID\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-31T17:00:32+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-07T08:38:26+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Relasi-dan-Fungsi.webp\" \/>\n\t<meta property=\"og:image:width\" content=\"800\" \/>\n\t<meta property=\"og:image:height\" content=\"533\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/webp\" \/>\n<meta name=\"author\" content=\"sereliciouz, Pamela Natasa, S.Pd.\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:site\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"sereliciouz\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.quipper.com\\\/id\\\/blog\\\/mapel\\\/matematika\\\/relasi-dan-fungsi\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/relasi-dan-fungsi\\\/\"},\"author\":{\"name\":\"sereliciouz\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/person\\\/b08224c7b72a87b156db30c3b032083b\"},\"headline\":\"Relasi dan Fungsi &#8211; 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