DIAGRAMVENN - Selamat Datang Di Kumpulan Materi Matematika SMP,SMA,SMK sebagai media Diagram Venn adalah salah satu cara menggambarkan suatu himpunan dalam bentuk diagram. Cara membuat diagram Venn adalah sebagai berikut. {1, 2, 3}, dan B = {x| 2 < x ≤ 5, x ∈ bilangan asli}. Coba gambarkan diagram Venn untuk menyatakan ketiga

Diagram Venn dan Himpunan Beserta Penjelasannya – Materi mengenai diagram venn dan himpunan mempunyai hubungan yang sangat erat. Sebab fungsi diagram venn bisa dipakai untuk menjelaskan bentuk-bentuk himpunan gabungan seperti irisan, selisih dan komplemen. Karena itulah pada kesempatan kali ini kita admin akan memberikan penjelasan mengenai diagram venn dan himpunan berikut penjelasannya. Untuk sobat semua yang belum tahu apa itu diagram venn ataupun himpunan, silahkan menyimak materi lengkap kali ini, sebab akan dijelaskan secara lengkap mengenai pengertian diagram venn, pengertian himpunan, cara menggambarkan diagram venn, dan macam-macam bentuk diagram venn dalam menyatakan suatu himpunan. Materi kali ini selengkapnya.. Contents 1 Diagram Venn Dan Himpunan2 Pengertian Diagram Venn3 Pengertian Himpunan4 Cara Menggambar Diagram Venn5 Macam – Macam Bentuk Diagram Venn6 Diagram Venn Saling Berpotongan7 Diagram Venn Saling Lepas8 Diagram Venn Himpunan Bagian9 Diagram Venn Himpunan Yang Sama10 Diagram Venn Ekuivalen11 Diagram Venn Gabungan Himpunan12 Diagram Venn Irisan Himpunan13 Diagram Venn Selisih14 Diagram Venn Komplemen Nah, sebagaimana yang dijelaskan diawal, kita akan mulai belajar dari pengertian diagram venn, pengertian himpunan dan contohnya untuk memudahkan memahaminya. Kita mulai dari.. Pengertian Diagram Venn Diagram venn yaitu diagram yang dipakai untuk menjelaskan hubungan antar himpunan yang mempunyai kesesuaian suatu kelompok. Penggunaan diagram venn sangat memudahkan dalam mempelajari hubungan antara himpunan. Secara umum, diagram venn dipakai untuk menggambarkan suatu himpunan yang saling berpotongan, saling lepas, ekuivalen, himpunan bagian dan himpunan yang sama. Atau bisa juga dipakai untuk menjelaskan bentuk-bentuk himpunan seperti gabungan himpunan, irisan, selisih dan komplemen. Untuk membuat atau membaca suatu diagram venn, sobat semua perlu memahami juga apa yang dimaksud dengan himpunan. Berikut ini adalah penjelasan mengenai pengertian himpunan beserta contohnya.. Pengertian Himpunan Himpunan diartikan sebagai kumpulan suatu obyek yang bisa didefinisikan dengan jelas dan bisa dinyatakan sebagai sebuah kesatuan. Himpunan biasa ditulis didalam kurung kurawal. Contohnya A = {0,1,2,3,4…}. Lebih mudahnya mengenai penjelasan himpunan, perhatikan penjelasan berikut.. Sebagai Contoh 1. Himpunan bilangan asli. 2. Himpunan lukisan yang bagus Dari contoh himpunan diatas, kita bisa mengetahui perbedaan antara himpunan dengan yang bukan himpunan. Berikut penjelasannya. Coba Perhatikan contoh 1, jika yang ditanya Himpunan bilangan asli, kita bisa dengan mudah menjawab dengan bilangan yang dimulai dari {1,2,3,4,5..}. Hal ini karena, himpunan asli mempunyai definisi yang jelas,sehingga bilangan asli termasuk dalam suatu bilangan. Sekarang ke contoh 2, dituliskan kata “Bagus” pada himpunan lukisan yang bagus, yang penilaian bagus tersebut tentunya berbeda untuk setiap orang yang berbeda. Sebagai contoh, kita anggap lukisan A bagus , Tapi menurut orang lain belum tentu sama dengan penilaian kita bukan? karena itulah lukisan yang bagus bukalah suatu himpunan, sebab tidak mempunyai definisi yang jelas. Baca Juga Contoh Soal Volume, Luas Permukaan dan Tinggi Tabung +Pembahasan Cara Menggambar Diagram Venn Setelah kita sama-sama belajar pengertian dari diagram venn dan himpunan, maka akan lanjut belajar menggambar diagram venn. Untuk mulai menggambar sebuah diagram venn, ada beberapa hal yang perlu diperhatikan, diantaranya yaitu.. Mengenal bentuk-bentuk himpunan. Sebab diagram venn biasanya menggambarkan suatu himpunan yang sedang dibicarakan. seperti gabungan, irisan, selisih, dan komplemen. Memahami himpunan semesta s yang dinyatakan dalam bentuk persegi panjang. Himpunan semesta yaitu semua anggota himpunan yang memuat himpunan yang sedang dibicarakan. Memahami himpunan lan yang dibicarakan. Biasanya dinyatakan dengan bentuk lingkaran atau kurva tertutup. Setiap anggota bisa ditulis dengan bentuk noktah / titik. Apabila ada anggota himpunan yang tak hingga, maka tiap-tiap anggota tidak perlu dinyatakan dengan titik. Macam – Macam Bentuk Diagram Venn Seperti yang dijelaskan yang lalu, bahwa membuat diagram venn kita perlu mengenal jenis-jenis himpunan. Jenis-jenis himpunan yang dibicarakan itulah yang menghasilkan bentuk diagram venn. Berikut ini beberapa bentuk-bentuk diagram venn.. Diagram Venn Saling Berpotongan Bentuk Diagram venn diatas adalah gambaran himpunan yang saling berpotongan. Contohnya jika himpunan A dan B mempunyai beberapa anggota yang sama, maka himpunan tersebut digambarkan dengan diagram venn yang saling berpotongan. Adapun area yang berpotongan merupakan anggota yang sama dari himpunan A dan himpunan B. Himpunan A yang berpotongan dengan Himpunan bilangan B bisa dituliskan dengan A ∩ B. Diagram Venn Saling Lepas Bentuk diagram diatas menggambarkan himpunan yang saling lepas. Contohnya himpunan A dan B tidak mempunyai anggota yang berbeda, sehingga disebut sebagai himpunan yang lepas. dan jika dinyatakan kedalam diagram venn maka akan terbentuk diagram venn saling lepas. Himpunan saling lepas bisa dituliskan dengan A // B. Diagram Venn Himpunan Bagian Bentuk diagram venn diatas, adalah gambaran himpunan bagian. Himpunan bagian yaitu himpunan yang anggotanya tersusun dari anggota himpunan lainnya. Contohnya, himpunan A bisa dikatakan bagian dari bagian himpunan B. Jika semua anggota himpunan bilangan A adalah anggota himpunan B, maka bisa dituliskan dengan A ⊂ B atau B ⊃ A. Baca Juga Contoh Soal Limas Volume dan Luas Permukaan Limas Diagram Venn Himpunan Yang Sama Bentuk diagram venn diatas adalah untuk menggambarkan himpunan yang sama. Himpunan tersebut menyatakan bahwa, himpunan A dan Himpunan Bilangan B mempunyai anggota himpunan yang sama. Mudahnya, Anggota himpunan bilangan A adalah anggota himpunan bilangan B dan Anggota himpunan bilangan B adalah anggota himpunan bilangan A. Himpunan sama ini bisa dituliskan dengan A = B. Diagram Venn Ekuivalen Bentuk diagram diatas merupakan gambaran untuk himpunan yang ekuivalen. sebagai contoh, Himpunan bilangan A dan B bisa disebut ekuivalen apabila banyaknya anggota dari kedua himpunan sama. himpunan A yang ekuivalen dengan Himpunan B bisa dituliskan dengan n A = n B. Dalam Soal matematika, diagram venn juga sering dipakai untuk menyatakan jenis-jenis himpunan seperti; gabungan, irisan, selisih, dan komplemen himpunan. Diagram Venn Gabungan Himpunan Gabungan Merupakan operasi himpunan yang seluruh anggotanya digabungkan menjadi himpunan baru, dan anggota yang sama hanya dituliskan satu kali. Himpunan A yang digabungkan dengan himpunan B, bisa dituliskan dengan A ∪ B = {x x ∈ A atau x ∈ B}. Sebagai Contoh A = {2, 3, 4, 5,} B = {4,5, 6, 7} A ∪ B = {2,3,4,5,6,7} Diagram Venn Irisan Himpunan Irisan yaitu sebuah operasi himpunan yang mana anggota himpunan A mempunyai beberapa anggota yang sama dengan himpunan B. Atau dengan kata lain, suatu himpunan yang anggotanya ada di kedua himpunan tersebut. Himpunan A yang ber irisan dengan Himpunan B dituliskan dengan A ∩ B = {x x ∈ A dan x ∈ B}. Sebagai Contoh A = {1,2,3,4,5,6} B = {5,6, 7,8} A ∩ B = {5,6} Diagram Venn Selisih Selisih dari himpunan A dengan himpunan B adalah seluruh anggota himpunan A, namun tidak dimiliki oleh anggota himpunan B. Himpunan yang selisih himpunan B, bisa dituliskan dengan A – B = {x x ∈ A atau x Ï B}. Sebagai Contoh A = {2,3,4,5,6,7} B = {4,5,7,12,5} A – B = {2,3,6} Diagram Venn Komplemen Komplemen dari himpunan A yaitu himpunan keseluruhan elemen dari himpunan semesta s, yang tidak ada di himpunan A. Himpunan komplemen A bisa dituliskan dengan A’ atau Ac = {x x ∈ S atau x Ï A}. Sebagai Contoh A = {5,6,7,8,9,10} S = {bilangan asli kurang dari 10} Ac = {1,2,3,4,} Demikianlah sobat, sedikit pembahasan mengenai diagram venn dan himpunan. Dan kesimpulannya yaitu diagram venn digunakan untuk menggambarkan hubungan antar himpunan. Semoga bermanfaat dan sampai jumpa lagi di kesempatan yang lain.. 😀😀😀

This is a Venn diagram using only one set, A This is a Venn diagram Below using two sets, A and B. This is a Venn diagram using sets A, B and C. Study the Venn diagrams on this and the following pages. It takes a whole lot of practice to shade or identify regions of Venn diagrams. Be advised that it may be necessary to shade several practice diagrams along the way before you get to the final result. We shade Venn diagrams to represent sets. We will be doing some very easy, basic Venn diagrams as well as several involved and complicated Venn diagrams. To find the intersection of two sets, you might try shading one region in a given direction, and another region in a different direction. Then you would look where those shadings overlap. That overlap would be the intersection. For example, to visualize \A \cap B\, shade A with horizontal lines and B with vertical lines. Then the overlap is \A \cap B\. The diagram on the left would be a first step in getting the answer. The shaded part on the diagram to the right shows the final answer. Here are two problems for you to try. Only shade in the final answer for each exercise. Exercise 1 Shade the region that represents \A \cap C\ Exercise 2 Shade the region that represents \B \cap C\ To shade the union of two sets, shade each region completely or shade both regions in the same direction. Thus, to find the union of A and B, shade all of A and all of B. The final answer is represented by the shaded area in the diagram to the right. Here are two problems for you to try. Only shade in the final answer for each exercise. Exercise 3 Shade the region that represents \A \cup C\ Exercise 4 Shade the region that represents \B \cup C\ For the complement of a region, shade everything outside the given region. You can think of it as shading everything except that region. On the Venn diagram to the left, the shaded area represents A. On the Venn diagram to the right, the shaded area represents . Many people are confused about what part of the Venn diagram represents the universe, U. The universe is the entire Venn diagram, including the sets A, B and C. The three Venn diagrams on the next page illustrate the differences between U, \U^{c}\ and \A \cup B \cup C^{c}\. Carefully note these differences. Usually, parentheses are necessary to indicate which operation needs to be done first. If there is only union or intersection involved, this isn’t necessary as in A \\cup\ B \\cup\ C\^{c}\ above. Convince yourself that A \\cup\ B \\cup\ C = A \\cup\ B \\cup\ C. Similarly, convince yourself of the analogous fact for intersection by performing the following steps. On the first Venn diagram below, shade A \\cap\ B with horizontal lines and shade C with vertical lines. Then, the overlap is A \\cap\ B \\cap\ C. On the second Venn diagram, shade A with lines slanting to the right and B \\cup\ C with lines slanting to the left. Then the overlap is A \\cap\ B \\cap\ C. Check to see that the final answer, the overlap in this case, is the same for both. Shade the final answer in the third Venn diagram. Exercise 5 a. A \\cap\ B \\cap\ C b. A \\cup\ B \\cup\ C c. Shade final answer here. Now, it's time for you to try a few more diagrams on your own. It may take more than one step to figure out the answer. You might need to do preliminary drawings on scratch paper first. The shadings you show here should be the final answer only, but you should be able to explain and support how you arrived at your answer. Compare your answers with other people in your class and make sure a consensus is reached on the correct answer. Do this for all the Venn diagrams throughout this exercise set. Shade in the region that represents what is written above each of the six Venn diagrams on the following page. Note that in cases involving more than one operation, it is necessary to use parentheses and follow order of operations. Exercises 10 and 11 illustrate why this is necessary. Exercise 6 B\^{c}\ Exercise 7 C \\cap\ A\^{c}\ Exercise 8 B \\cup\ C\^{c}\ Exercise 9 A \\cap\ B \\cap\ C\^{c}\ Exercise 10 A \\cap\ B \\cap\ C Exercise 11 A \\cap\ B \\cap\ C For difference, shade the region coming before the difference sign – but don’t include or shade any part of the region that follows the difference sign. The Venn on the left represents A–B and the one on the right represents C–A. Here are two problems for you to try. Only shade in the final answer for each exercise. Exercise 12 Shade the region that represents A – C Exercise 13 Shade the region that represents B – C Study the following Venn diagrams. Make sure you understand how to get the answers. A \\cup\ B – C C – A \\cap\ B A\^{c}\ – B \\cap\ C It's your turn to shade in the region that represents what is written above each diagram. Exercise 14 A \\cap\ C – B Exercise 15 B – A \\cap\ C Exercise 16 A – C \\cup\ B – A Suppose you wanted to find C – A \\cap\ B\^{c}\. This would probably take a few steps to get the answer. One approach to finding the correct shading is to notice that the final answer is the complement of C – A \\cap\ B. That means we would have to first figure out what C – A \\cap\ B looked like. In order to do that, we notice that this is the intersection of two things C – A and B. On the blank Venn diagram to the left below, shade C – A with horizontal lines and B with vertical lines. The overlap would be the intersection. The overlap on your drawing should match the shading shown on the Venn diagram in the middle. Does it? The last step would then be to take the complement of the shading shown on the middle diagram. This is shown on the Venn diagram on the far right. So, it took drawing three Venns to come up with the final answer for this problem. Someone else might be able to do it in fewer steps while someone else might take more steps. Exercise 17 C – A \\cap\ B C – A \\cap\ B\^{c}\ As mentioned previously, it takes a lot of practice to get good at shading Venn diagrams. It’s even trickier to look at a Venn diagram and describe it, In fact, there is usually more than one way to describe a Venn diagram. For example, the shading for C – A \\cap\ B\^{c}\ shown on the previous page is the same as it is for C \\cap\ B – A\^{c}\. What does this mean? We’re so used to only having one correct answer. Well, consider if someone asked you to write an arithmetic problem for which the answer was 2. There would be infinitely many possibilities. For example, 5 - 3 or 1 + 1 or 10/5 would all be acceptable answers. Granted, this kind of question on a test would be harder for a teacher to grade because each student’s response would have to be checked to see if it would work. There isn’t one pat answer. The same goes if a teacher asks you to look at a shading of a Venn diagram and describe it. On the other hand, if a description is given and you are asked to shade the Venn diagram, there is only one correct shading. It is much like being asked to compute an arithmetic problem. The answer to 10 - 8 is 2 and that is the only acceptable answer! The point of all this is that to master shadings of Venn diagrams and descriptions of Venn diagrams by looking at the shadings takes lots and lots and lots of practice. Give yourself plenty of time to study and work on them and you will accomplish this feat!!! On the next few pages, you are asked to shade several one, two and three set Venn diagrams. The correct shadings follow. Make sure you try these problems in earnest. Make sure you can explain the steps involved to arrive at the correct shading. After mastering the shadings, see if you can look at a shaded Venn diagram and come up with an accurate description. Again, remember there is more than one way to describe a given Venn diagram. These Venn diagrams will be helpful when studying for a test. Go back and practice drawing the same Venn diagrams later. Use the answers to see if you can describe them by looking at the picture. Of course, remember that your description might not match exactly since there as more than one way to describe any given Venn diagram. If your description is different, make sure you go through the steps of shading a Venn with your description and see if your shading really matches the Venn diagram you were trying to describe. Here are a few shaded Venn diagrams. See if you can look at the shadings and come up with a description. I’ve put some possible answers at the bottom of this page. Here are some possible descriptions for the above Venn diagrams C – B\^{c}\ A \\cup\ C\^{c}\ A \\cap\ C\^{c}\ Shade the region that represents what is written above each of the one and two set Venn diagrams below. You may need to draw preliminary drawings first for some of them. Exercise 18 A Exercise 19 \A^{c}\ Exercise 20 U Exercise 21 \U^{c}\ Exercise 22 A \\cap\ B Exercise 23 A \\cup\ B Exercise 24 \A \cup B^{c}\ Exercise 25 \A \cap B^{c}\ Exercise 26 \A \cup B^{c}\ Exercise 27 A \B \\cup\ B \A Exercise 28 \A^{c} \cup B^{c}\ Exercise 29 \A^{c} \cap B^{c}\ Exercise 30 \A \cup B^{c} \cup A \cap B\ Exercise 31 B Exercise 32 B - A Exercise 33 \B^{c}\ Shade the region that represents what is written above each of the one and two set Venn diagrams below. You may need to draw preliminary drawings first for some of them. Exercise 34 A \\cap\ B – C Exercise 35 C \\cup\ B – A Exercise 36 A \\cap\ B \\cup\ C Exercise 37 A \\cup\ B \\cap\ C Exercise 38 A\^{c}\ – B Exercise 39 A \\cap\ B \\cap\ C – B Exercise 40 B – A \\cup\ C Exercise 41 C – A \\cap\ B Exercise 42 B – A \\cap\ B – C Exercise 43 B – A \\cup\ B – C Exercise 44 A \\cup\ B\^{c}\ Exercise 45 A\^{c}\ \\cap\ B\^{c}\ Exercise 46 A\^{c}\ – B\^{c}\ Exercise 47 C – B\^{c}\ Exercise 48 B\^{c}\ \\cap\ C – A Exercise 49 A – B \\cup\ C \\cup\ B – A \\cup\ C \\cup\ C – A \\cup\ B Exercise 50 A \\cap\ C\^{c}\ Exercise 51 A \\cap\ B – C \\cap\ C – A Exercise 52 A\^{c}\ \\cup\ C\^{c}\ Exercise 53 B \\cap\ C \\cup\ A\^{c}\ Here are the correct shadings to the exercises on the previous pages. After mastering these shadings, reverse the process by looking at the shadings on this page and try to describe them. It takes practice and patience and remember that there may be more than one way to describe some of these. In fact, many times you'll see there is a simpler way to describe them than was on the original exercise!! 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. Nothing is shaded. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. Nothing is shaded. 52. 53. In the Material Card section there are blank Venn diagram templates you can use for practice.

diagram venn bentuk 1 dan diagram venn bentuk 2