{"id":304895,"date":"2021-11-01T00:00:02","date_gmt":"2021-10-31T17:00:02","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=304895"},"modified":"2022-10-14T14:28:54","modified_gmt":"2022-10-14T07:28:54","slug":"operasi-himpunan","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/operasi-himpunan\/","title":{"rendered":"Pengertian Himpunan &#8211; Cara Menyajikan, Sifat Operasi Himpunan dan Contoh Soal"},"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\/Pengertian-Himpunan-copy.webp\" alt=\"\" class=\"wp-image-304902\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Himpunan-copy.webp 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Himpunan-copy-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Himpunan-copy-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Himpunan-copy-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;\">Pernahkah kamu mendengar istilah himpunan? Misalnya, kamu mengelompokkan kambing, sapi, kerbau, kuda, kucing ke dalam kelompok hewan berkaki empat. Nah, itu sama artinya kamu membuat suatu himpunan hewan berkaki empat. Sama seperti bilangan, himpunan juga bisa dioperasikan. Lantas, seperti apa operasi himpunan itu? Simak ulasan selengkapnya!<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Pengertian Himpunan<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Himpunan adalah kumpulan objek atau benda yang memiliki karakteristik yang sama dan bisa didefinisikan dengan jelas. Contohnya himpunan hewan berkaki empat, himpunan pembentuk kata \u201cQuipper\u201d, dan sebagainya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Himpunan biasa dituliskan dengan kurung kurawal {}. Di dalam kurung kurawal ditulis anggota-anggota yang memenuhi. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Himpunan hewan berkaki empat = {kambing, sapi, kerbau, kuda, kucing}<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Himpunan pembentuk kata \u201cQuipper\u201d = {Q, U, I, P, E, R} <\/span><span style=\"font-weight: 400;\">-&gt;<\/span><span style=\"font-weight: 400;\"> untuk huruf P cukup ditulis satu saja, ya.<\/span><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Cara Menyajikan Himpunan<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Himpunan bisa disajikan ke dalam tiga bentuk, yaitu sebagai berikut.<\/span><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Enumerasi, yaitu dengan menuliskan anggotanya ke dalam kurung kurawal seperti contoh sebelumnya.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Menuliskan sifat anggotanya, misal B = himpunan bilangan genap yang kurang dari 10.<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Membuat notasi anggota himpunan, misal B = {<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">|<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> &lt; 10, <\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\"> adalah bilangan genap}<\/span><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Seluruh anggota himpunan yang saling berhubungan bisa dinyatakan dalam suatu diagram yang disebut diagram Venn. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"314\" height=\"245\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Operasi-Himpunan-a.webp\" alt=\"\" class=\"wp-image-304899\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Keterangan:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">S = himpunan semesta&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">&nbsp;&nbsp;&nbsp;= {a, b, c, d, e}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {b, d, e}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Artinya, A merupakan bagian dari S atau biasa ditulis A <\/span><span style=\"font-weight: 400;\">\u2282<\/span><span style=\"font-weight: 400;\"> S.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Operasi Himpunan<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Sama seperti bilangan, himpunan juga bisa dioperasikan. Adapun bentuk operasi himpunan adalah sebagai berikut.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>1. Irisan<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika Quipperian punya dua himpunan, misal C dan D. Nah, ternyata ada anggota C yang juga anggota D. Anggota yang sama-sama dimiliki kedua himpunan itulah yang dinamakan irisan atau biasa dilambangkan <\/span><span style=\"font-weight: 400;\">\u2229. <\/span><span style=\"font-weight: 400;\">Jika ditulis dalam bentuk notasi menjadi C <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> D = {<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i><span style=\"font-weight: 400;\">|<\/span><i><span style=\"font-weight: 400;\">x<\/span><\/i> <span style=\"font-weight: 400;\">\u2208<\/span><span style=\"font-weight: 400;\"> C dan <\/span><i><span style=\"font-weight: 400;\">x <\/span><\/i><i><span style=\"font-weight: 400;\">\u2208<\/span><\/i> <span style=\"font-weight: 400;\">D}.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">C = {2, 4, 6, 8}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">D = {1, 2, 3, 4, 5, 6}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Ternyata, ada anggota C yang sama dengan D, yaitu 2, 4, 6. Dengan demikian,<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">C <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> D = {2, 4, 6}.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>2. Gabungan (union)<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gabungan adalah total seluruh anggota dari dua himpunan atau lebih. Gabungan biasa dilambangkan dengan <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\">. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">C = {2, 4, 6, 8}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">D = {1, 2, 3, 4, 5, 6}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">C <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> D = {1, 2, 3, 4, 5, 6, 8}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Nah, hasil dari C <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> D itu disebut dengan himpunan semesta.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Ketentuan yang berlaku pada gabungan adalah sebagai berikut.<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>3. Komplemen<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Komplemen himpunan B adalah semua anggota himpunan semesta (S) yang bukan anggota himpunan B. Komplemen ini biasa dinyatakan sebagai <\/span>B<sup>C<\/sup><span style=\"font-weight: 400;\">. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">S = {A, <\/span><span style=\"color: #ff0000;\"><b>K<\/b><span style=\"font-weight: 400;\">, <\/span><b>U<\/b><\/span><span style=\"font-weight: 400;\">, B, L, J, <\/span><span style=\"color: #ff0000;\"><b>R<\/b><\/span><span style=\"font-weight: 400;\">}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {A, B, L, J}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B<sup>C<\/sup><span style=\"font-weight: 400;\"> = {K, U, R}<\/span><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>4. Selisih<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Misalkan ada dua himpunan, yaitu A dan B. Selisih menunjukkan komplemen relatif B terhadap A atau sebaliknya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Semua anggota himpunan A yang tidak termasuk anggota himpunan B disebut komplemen relatif B terhadap A. Secara matematis, dituliskan A \u2013 B.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {1, 3, <\/span><span style=\"text-decoration: underline;\"><strong>5<\/strong><\/span><span style=\"font-weight: 400;\">, 7, 9, <\/span><span style=\"text-decoration: underline;\"><strong>11<\/strong><\/span><span style=\"font-weight: 400;\">}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {1, 3, 7, 9}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A \u2013 B = {5, 11}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Sifat yang berlaku pada selisih adalah sebagai berikut.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Untuk A <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> B = <\/span><span style=\"font-weight: 400;\">\u2205<\/span><span style=\"font-weight: 400;\">, berlaku A \u2013 B = A atau B \u2013 A = B.<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Misal:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {4, 6, 8}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {7, 9, 11}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A \u2013 B = {4, 6, 8}<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Untuk A <\/span><span style=\"font-weight: 400;\">\u2282 <\/span><span style=\"font-weight: 400;\">B, berlaku A \u2013 B = <\/span><span style=\"font-weight: 400;\">\u2205.<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Misal:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {3, 5 ,7}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {1, 3, 5, 7, 8}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A \u2013 B = {0} <\/span><span style=\"font-weight: 400;\">-&gt;<\/span><span style=\"font-weight: 400;\"> himpunan kosong atau tidak ada anggotanya.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Sifat Operasi Himpunan<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Operasi himpunan memenuhi sifat-sifat berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">1. Pada sembarang himpunan P berlaku sifat berikut.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> P = P dan P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> P = P (sifat idempoten)<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">P <\/span><span style=\"font-weight: 400;\">\u222a<\/span> <span style=\"font-weight: 400;\">\u2205<\/span><span style=\"font-weight: 400;\"> = P dan P <\/span><span style=\"font-weight: 400;\">\u2229<\/span> <span style=\"font-weight: 400;\">\u2205<\/span><span style=\"font-weight: 400;\"> = P (sifat identitas)<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">2. Pada sembarang himpunan P dan Q berlaku sifat berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> Q = Q <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> P dan P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> Q = Q <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> P (sifat komutatif)<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">3. Pada sembarang himpunan P, Q, dan R berlaku sifat berikut.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> (Q <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> R) = (P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> Q) <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> R dan P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> (Q <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> R) = (P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> Q) <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> R (sifat asosiatif)<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> (Q <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> R) = (P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> Q) <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> (P <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> R) dan P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> (Q <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> R) = (P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> Q) <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> (P <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> R) (sifat distributif)<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Untuk mengasah pemahamanmu tentang operasi himpunan, simak contoh soal berikut ini.<\/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;\">Perhatikan dua himpunan berikut.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">F = {A, K, U, P, I, N, T, R}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">G = {D, I, A, P, N, T, R}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan irisan, gabungan, F \u2013 G, dan G \u2013 F!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pembahasan:<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Irisan F <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> G<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">F <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> G = {A, I, P, N, T, R}<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Gabungan F <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> G<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">F <\/span><span style=\"font-weight: 400;\">\u222a<\/span><span style=\"font-weight: 400;\"> G = {A, D, K, U, P, N, T, R}<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">F \u2013 G, yaitu semua anggota himpunan F yang tidak termasuk anggota himpunan G<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">F \u2013 G = {K, U}<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">G \u2013 F, yaitu semua anggota himpunan G yang tidak termasuk anggota himpunan G<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">G \u2013 F = {D}<\/span><\/p>\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;\">Jika A = {5, 10, 15, 20, \u2026, 100} dan B = {15, 30, 45, \u2026, 90}, tentukan nilai <\/span><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\">(A + B)!<\/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;\">Tentukan semua anggota himpunan A.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">A = {5, 10, 15, 20, \u2026, 100}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Himpunan A merupakan himpunan bilangan bulat kelipatan 5, mulai 5 sampai 100. Artinya:<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"157\" height=\"76\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Operasi-Himpunan-b.webp\" alt=\"\" class=\"wp-image-304898\"\/><\/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;\">Tentukan semua anggota himpunan B.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">B = {15, 30, 45, 60, 75, 90}<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\">(B) = 6<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika diperhatikan, B <\/span><span style=\"font-weight: 400;\">\u2282 <\/span><span style=\"font-weight: 400;\">A dan A + B adalah himpunan anggota A atau B, namun bukan anggota A <\/span><span style=\"font-weight: 400;\">\u2229<\/span><span style=\"font-weight: 400;\"> B, maka:<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\">(A + B) = <\/span><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\">(A) \u2013 <\/span><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\">(B) = 20 \u2013 6 = 14.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, <\/span><span style=\"font-weight: 400;\">nilai <\/span><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\">(A + B) = 14.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Itulah pembahasan Quipper Blog kali ini. Semoga bisa bermanfaat buat Quipperian. Jika kamu ingin mendapatkan materi operasi himpunan lebih lanjut, silakan gabung bersama <\/span><a href=\"https:\/\/subscribe.quipper.com\/signup\"><b>Quipper Video<\/b><\/a><span style=\"font-weight: 400;\">. Kamu bisa belajar bersama para tutor andal lewat tayangan video, rangkuman materi, contoh soal dan pembahasannya. Seru banget, kan! Buruan daftar, ya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Penulis: Eka Viandari<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pernahkah kamu mendengar istilah himpunan? Misalnya, kamu mengelompokkan kambing, sapi, kerbau, kuda, kucing ke dalam kelompok hewan berkaki empat. Nah, itu sama artinya kamu&hellip;<\/p>\n","protected":false},"author":99400369,"featured_media":304902,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[],"ppma_author":[679386827],"class_list":["post-304895","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 v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Himpunan - Cara Menyajikan, Sifat Operasi Himpunan dan Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Belajar himpunan, simak pengertianya apa? serta cara menyajikan himpunan berdasarkan sifat operasi himpunan lengkap dengan soal pembahasannya\" \/>\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\/operasi-himpunan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pengertian Himpunan - Cara Menyajikan, Sifat Operasi Himpunan dan Contoh Soal - Quipper Blog\" \/>\n<meta property=\"og:description\" content=\"Belajar himpunan, simak pengertianya apa? serta cara menyajikan himpunan berdasarkan sifat operasi himpunan lengkap dengan soal pembahasannya\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/operasi-himpunan\/\" \/>\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=\"2021-10-31T17:00:02+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-10-14T07:28:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/09\/Pengertian-Himpunan-copy.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\" \/>\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=\"4 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\\\/operasi-himpunan\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/operasi-himpunan\\\/\"},\"author\":{\"name\":\"sereliciouz\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/person\\\/b08224c7b72a87b156db30c3b032083b\"},\"headline\":\"Pengertian Himpunan &#8211; 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