{"id":130722,"date":"2017-05-26T12:49:48","date_gmt":"2017-05-26T05:49:48","guid":{"rendered":"https:\/\/video.quipper.com\/id\/blog\/?p=130722"},"modified":"2017-05-26T12:49:48","modified_gmt":"2017-05-26T05:49:48","slug":"yuk-belajar-matematika-dasar-sbmptn-tentang-teori-relasi","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/masuk-ptn\/sbmptn\/matematika-sbmptn\/yuk-belajar-matematika-dasar-sbmptn-tentang-teori-relasi\/","title":{"rendered":"Yuk Belajar Matematika Dasar SBMPTN Tentang Teori Relasi"},"content":{"rendered":"

\"\"<\/a><\/p>\n

Quipperian! Matematika Dasar SBMPTN selalu tidak lepas dengan Hubungan sebuah Himpunan. Dalam hal ini, Himpunan akan selalu berhubungan dengan variabel lain. Makanya, sangat penting untuk belajar tentang Teori Relasi. <\/span><\/p>\n

Teori Relasi ini bisa kita mulai pelajari dari produk Cartesius yang menjelaskan sebuah relasi hubungan Himpunan yang selalu berkaitan dengan variabel lain. Yuk belajar!<\/span><\/p>\n

Definisi Relasi<\/b><\/h2>\n

Sebelum mendefinisikan produk Cartesius, terlebih dahulu Anda perlu mengenal pengertian pasangan terurut. Dalam sistem koordinat Cartesius dengan sumbu x dan sumbu y, kita mengetahui bahwa titik dengan koordinat tidaklah sama dengan titik yang berkoordinat . <\/span><\/p>\n

Begitu pula titik lainnya tidak berimpit letaknya maka kedua titik ini tidak sama. Dalama hal koordinat titik seperti contoh di atas ternyata bahwa urutan pasangan bilangan itu harus diperhatikan karena urutan yang berlainan akan menentukan letak (posisi) titik dalam bidang XOY yang berbeda pula. <\/span><\/p>\n

Sepasang bilangan x dan y dengan x dalam urutan pertama dan y dalam urutan kedua, ditulis (x, y) dan dinamakan pasangan terurut. Selain itu, perlu pula untuk kita ketahui tentang perbedaan pasangan terurut (x,y) dengan himpunan {x, y}. Himpunan {x, y} sama dengan {y, x} karena dalam himpunan urutan tidak dipentingkan.<\/p>\n

<\/span><\/p>\n

Tips Ikut Les Privat Matematika Murah Tapi Tetap Berkualitas<\/a><\/h3>\n

Sekarang kita perhatikan A dan B sebagai dua himpunan yang diketahui. Dari kedua himpunan ini kita dapat membentuk suatu himpunan baru yang anggota-anggotanya merupakan pasangan terurut yang unsur pertamanya adalah anggota-anggota A dan unsur keduanya adalah anggota-anggota B. <\/span><\/p>\n

Himpunan yang baru dibentuk ini dinamakan Produk Cartesius (produk cartesius) dari A ke B atau disebut pula himpunan perkalian dari A ke B, dan ditulis A x B dibaca \u201cA kros B\u201d atau \u201cA kali B\u201d atau \u201cA silang B.\u201d<\/span><\/p>\n

\u201cJika A dan B dua himpunan maka produk Cartesius dari A ke B adalah himpunan semua pasangan trurut (x, y) dengan x \u00a0A, y \u00a0B yang ditulis A x B = {(x, y)\u2502x \u00a0A, y \u00a0B}\u201d<\/i><\/b><\/p>\n


\n<\/i><\/b>Contoh:<\/span><\/p>\n

    \n
  1. Andaikan kita dapat membeli suatu model sepeda motor dengan warna pilihan tertentu maka dapat kita pandang model dan warna tersebut sebagai unsur produk Cartesius dua himpunan yaitu model sepeda motor dan warna. Misalnya, unsur produk Cartesius itu adalah (vespa, biru), (honda, merah), (suzuki, hitam), dan sebagainya. <\/span><\/li>\n
  2. Jika R = {x\u2502x himpunan bilangan real} maka R x R merupakan himpunan semua pasangan terurut (a, b) dengan a \u00a0R dan b \u00a0R yang salah satunya dapat dituliskan oleh salah satu titik P(a, b) pada bidang XOY seperti Gambar 4.8:<\/span><\/li>\n<\/ol>\n

    \"Yuk<\/a><\/p>\n

    Istilah \u201crelasi\u201d yang dapat diartikan \u201chubungan\u201d sudah sering kalian dengar, misalnya \u201cayah\u201d dengan \u201canak\u201d, hubungan \u201cguru\u201d dengan \u201cmurid\u201d, dan sebagainya. Dalam matematika, untuk mendefinisikan sebuah relasi, kita perlu memahami pengetian tentang himpunan, pasangan terurut, perkalian himpunan (produk cartesius) dan kalimat terbuka. Materi-materi ini tentunya telah kita pelajari. <\/span><\/p>\n

    Sebaiknya Ikut Les Privat Matematika Sejak Kelas Berapa Sih?<\/a><\/h3>\n

    Untuk mendefinisikan suatu relasi R diperlukan: <\/span><\/p>\n

      \n
    1. suatu himpunan A <\/span><\/li>\n
    2. suatu himpunan B <\/span><\/li>\n
    3. suatu aturan atau kalimat matematika terbuka. <\/span><\/li>\n<\/ol>\n

      Untuk lebih jelasnya perhatikan uraian berikut, misalnya: <\/span><\/p>\n

        \n
      1. himpunan tiga orang siswa SMP: A = {Ajid, Enal, Aulia} <\/span><\/li>\n
      2. himpunan nomr sepatu: B = {37, 38, 39, 40, 41} Diketahui bahwa: Ajid memakai sepatu nomor 40 \u25cf x b a P(a,b) y 55 Enal memakai sepatu nomor 38 Aulia memakai sepatu nomor 38 Dari keterangan di atas dapat kita tentukan suatu relasi dari himpunan orang (A) ke himpunan nomor sepatu (B) yang relasinya disebut \u201cnomor sepatunya\u201d atau \u201cmemakai sepatu nomor\u201d.<\/span><\/li>\n<\/ol>\n

        Bila relasi di atas dinyatakan dengan diagram panah maka dapat dilihat pada Gambar 4.9:<\/span><\/p>\n

        \"Yuk<\/a><\/p>\n

        Tanda panah menyatakan anggota-anggota yang berelasi, dan anak panah menunjukkan arah relasi tersebut, yaitu dari A ke B. Arah itu tidak boleh terbalik, sebab relasi dari A ke B tidak sama dengan relasi dari B ke A. <\/span><\/p>\n

        Relasi di atas dapat pula dinyatakan dalam bentuk pasangan terurut, misalnya \u201c Ajid memakai sepatu nomor 40\u201d cuku ditulis singkat (Ajid, 40). Demikian pula untuk yang lainnya. Jadi relasi tersebut bila kita tulis dengan bentuk pasangan terurut adalah: <\/span><\/p>\n

        R = {(Ajid, 40), (Enal, 38), (Aulia, 38)}<\/p>\n

        <\/span><\/p>\n

        \u201cRelasi R dengan suatu kalimat terbuka dari himpunan A ke himpunan B adalah sebuah himpunan yang anggota-anggotanya semua pasangan terurut (x, y) dengan x \u00a0A dan y \u00a0B sedemikian rupa sehingga kalimat terbukanya menjadi benar.\u201d<\/i><\/b><\/p>\n

         <\/p>\n

        Penulis: Sritopia<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

        Quipperian! Matematika Dasar SBMPTN selalu tidak lepas dengan Hubungan sebuah Himpunan. Dalam hal ini, Himpunan akan selalu berhubungan dengan variabel lain. Makanya, sangat penting…<\/p>\n","protected":false},"author":156446345,"featured_media":130732,"comment_status":"open","ping_status":"open","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,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[253044991],"tags":[169291195],"ppma_author":[679386822],"class_list":["post-130722","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika-sbmptn","tag-contoh-soal-sbmptn"],"acf":[],"yoast_head":"\nYuk Belajar Matematika Dasar SBMPTN Tentang Teori Relasi<\/title>\n<meta name=\"description\" content=\"Quipperian, Matematika Dasar bisa jadi sangat membingungkan. 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