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- Sets and Venn Diagrams
- Sets and Venn Diagrams

*Mathematicians use Venn diagrams to show the logical relationships of sets collections of objects to one another.*

Each friend is an "element" or "member" of the set. It is normal to use lowercase letters for them. It says the Set "Soccer" is made up of the elements alex, casey, drew and hunter.

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Notice, there were rectangles around those examples. Those rectangles represented the universal set.

All the elements under discussion. To represent a single set, such as A. I would draw one circle and shade it in. I'm glad you asked. Just like before, the complement of A are all the members of the universal set not in A.

Let's look at the set difference. Remember A -B was defined as all the elements in A, but couldn't belong to B. Again, the illustrations are important, introducing a third set using a circle does not in any way change what we have already defined.

In fact, if there is a third set, we work with just two at a time, just like we did with sets. After that, we take that result and intersect it with C. Where the shading overlaps is what these sets have in common. That almost makes sense, for an element to belong to A, B and C, there is only one region within the three circles that satisfies that. Now, we'll describe each region. What about Region 2? Those are the elements in A and B, but not C.

How might you describe Region 6? Those are elements in B and C, but not in A. Try Region 4. The elements in A and C, but not B. This is fun, let's look at some more regions.

Region 1 describes the elements in A only. What about region 3? Those elements are only in B. Region 7 then would be the elements in C only. Region 8 would describe elements that are not members of any of the sets, but belong to the universal set.

It's important that you become familiar with how each of those regions might be described. Being able to describe those regions would allow you to solve some problems.

ExampleA survey was taken of university students. It was reported that were taking math, were taking biology, and were enrolled in chemistry.

Of those students, 80 were taking biology and math, 70 were taking math and chemistry, 60 were taking biology and chemistry, and 50 were taking all three classes. How many students took math only? At first glance, you might not think this is possible because the numbers add up to more than But if you are familiar with how the regions are described, we can determine how many were in each region.

In going about this problem, I would tell you to draw a Venn Diagram and begin by filling in Region 5, the students that took all three courses. U M B C 50After doing that, we'll place the number of students taking each course on the circle because we don't know where those students should be located within the circles.

Okay, now we can have some fun by determining what regions the students should be located. For instance, it says that 80 students are taking math and biology. We have 50 of those accounted for in Region 5, how many does that leave to be in Region 2? Using that same reasoning, 70 students are taking math and chemistry, how many students would then be in Region 4?

That's pretty easy, don't you think? Ok, how many students should be in Region 6? Since there are 60 students enrolled in biology and chemistry, and 50 of them are accounted for in Region 5, that leaves 10 students for Region 6. Let's fill in those numbers: Now how many students would be in Region 1?

Now remember, there are supposed to be students taking math, we have accounted for in Regions 2, 4, and 5. That leaves students in region 1, taking math only. How many students are taking biology only? Well, we were told that students were taking biology, we have 90 of them accounted for in Regions 2, 5, and 6, that leaves students in Region 3.

How many are taking only chemistry? We know there are students taking chemistry, we have 90 accounted for in Regions 4, 5, and 6, that leaves in Region 7. Filling in those numbers and taking the numbers off the circle, we have the following information. We have one slight problem, if we add those regions within the circles, the total is students. The problem stated were surveyed, we're missing ten students. Where are they? That's right, they would be in Region 8, not taking any of those courses.

Now tell me, was that fun? How many students took math and biology, but not chemistry? How many students took math and chemistry, but not biology? How many students took biology and chemistry, but not math? How many students took only math? How many students took exactly two of the courses? A local merchant uses television, radio, and newspaper advertising. To determine the effectiveness of advertising, he questions customers during a special afterhours sale to see how they knew about the sale.

He found that had seen television ads, 75 had heard radio ads, and had read newspaper ads. He also found that 30 received information from television and radio, 70 from television and newspapers, 25 from radio and newspapers, and 10 from all three.

If everyone else said they heard it from a friend, how many heard it from a friend? In order to prepare a report on agricultural prospects for his county, the county farm advisor questions farmers about their crop plans for the following year.

He finds that 75 intend to plant corn, 55 will plant soybeans, 35 will plant wheat, 35 will plant corn and soybeans, 25 will plant corn and wheat, 15 will plant soybeans and wheat, and 10 will plant all three. How many of the farmers will plant only one crop? How many will plant at least two crops? In a group of primary students, watch "Sesame Street," 55 watch "Electric Company," and 65 watch "Mr.

Rogers' Neighborhood. Rogers," 30 watch "Electric company" and "Mr. Rogers," and 20 watch all three, how many watch none of the three? How many watch only "Sesame Street"? So any elements in region 5 would belong to all three sets. Related Papers. By Kara Fleming. Language attitudes and identities in multilingual China. By Sihua Liang. By Veronica Needa. By Christian A Hesse. By Alan Deyoung.

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To understand, how to solve venn diagram word problems with 3 circles, we have to know the following basic stuff. Theorem 2 :. Explanation :. In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry , 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only. Solution :.

Abbreviations are fine. Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance 1. About this resource. The purpose of this module is to introduce language for talking about sets, and some.

It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. We can use these sets understand relationships between groups, and to analyze survey data. An art collector might own a collection of paintings, while a music lover might keep a collection of CDs. Any collection of items can form a set.

Download transcript. Tropical rainforests are bursting with diversity and life, whereas deserts seem barren and desolate. In this case, the characteristics of the two environments will be placed within their appropriate sets. Rainforests are covered in thick vegetation w hereas in deserts plant life can be very sparse. The rainforest is home to many unique species, such as the poison arrow frog, the bird of paradise, and the howler monkey.

An extensive collection of Venn diagram worksheets provided here will help students of grade 2 through high school to use their analytical skills and study all possible logical relations between a finite collection of sets. A number of interesting cut and paste and surveying activity worksheets are up for grabs! A plethora of exercises that include finding, shading, and naming unions, intersections, differences, and complements are provided here. Some of them might require representing the Boolean operation between the given sets. Exclusive pdf worksheets on completing Venn diagrams based on a given set of data are also available for practice. Kick-start your Venn diagram practice with our free worksheets! These printable cut-and-glue activity worksheets based on different themes will keep 2nd grade and 3rd grade children thoroughly engaged.

Each group is represented using a circle. The Venn diagram for the set difference of sets A and B is shown below where the shaded region represents A — B. A Venn Diagram is a way to present logical relationships between people or things in a picture. Creately diagrams can be exported and added to Word You can use this example diagram as a template to illustrate the logical relationships between two or more sets of items.

Сьюзан подбежала к. - Коммандер. Стратмор даже не пошевелился. - Коммандер. Нужно выключить ТРАНСТЕКСТ. У нас… - Он нас сделал, - сказал Стратмор, не поднимая головы.

Теперь же он был рад, что проделал это, потому что на мониторе Сьюзан скрывалось что-то очень важное. Задействованная ею программа была написана на языке программирования Лимбо, который не был его специальностью. Но ему хватило одного взгляда, чтобы понять: никакая это не диагностика. Хейл мог понять смысл лишь двух слов. Но этого было достаточно. СЛЕДОПЫТ ИЩЕТ… - Следопыт? - произнес. - Что он ищет? - Мгновение он испытывал неловкость, всматриваясь в экран, а потом принял решение.

Ты не заметил ничего. Ну, может, дошел какой-нибудь слушок. - Мидж, послушай. - Он засмеялся. - Попрыгунчик - древняя история. Стратмор дал маху. Но надо идти вперед, а не оглядываться все время .

Она повернулась к монитору и показала на работающего Следопыта. - Я никуда не спешу. Стратмор сокрушенно вздохнул и начал мерить шагами комнату. - Очевидно, когда Танкадо умер, рядом находились свидетели. Согласно словам офицера, который отвел Дэвида в морг, некий канадский турист сегодня утром в панике позвонил в полицию и сказал, что у одного японца в парке случился сердечный приступ.

Сьюзан наклонилась к Дэвиду и шепнула ему на ухо: - Доктор. Он смотрел на нее с недоумением. - Доктор, - повторила .

*У нее оставалось целых пять часов до рейса, и она сказала, что попытается отмыть руку. - Меган? - позвал он и постучал. Никто не ответил, и Беккер толкнул дверь.*

Нуматака проследовал прямо на коммутатор компании. Все звонки принимались единственным оператором на двенадцатиканальный терминал Коренсо-2000. Телефонистка, державшая трубку у уха, мгновенно поднялась и поклонилась, увидев босса. - Садитесь! - рявкнул Нуматака. Она опустилась на стул.

Клушар продолжал бушевать: - И этот полицейский из вашего города тоже хорош. Заставил меня сесть на мотоцикл. Смотрите сюда! - Он попытался поднять левую руку. - Кто теперь напишет материал для моей колонки. - Сэр, я… - За все сорок три года путешествий я никогда еще не оказывался в таком положении.

- Я не расслышал, как тебя зовут. - Двухцветный, - прошипел панк, словно вынося приговор. - Двухцветный? - изумился Беккер.

- Гамма-лучи против электромагнитной пульсации. Распадающиеся материалы и нераспадающиеся. Есть целые числа, но есть и подсчет в процентах.