# Set Operations And Venn Diagrams Pdf

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How do you find the intersection of a Venn diagram? What is the best way to represent multiple set intersections visually, as Venn diagram is not good for more than sets?.

Solved basic word problems on sets:. Different types on word problems on sets:. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks.

## Sets and Venn Diagrams

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. A set is a collection of distinct objects, called elements of the set.

A set can be defined by describing the contents, or by listing the elements of the set, enclosed in curly brackets. A set simply specifies the contents; order is not important. Commonly, we will use a variable to represent a set, to make it easier to refer to that set later. Sometimes a collection might not contain all the elements of a set. For example, Chris owns three Madonna albums. A subset of a set A is another set that contains only elements from the set A , but may not contain all the elements of A.

A proper subset is a subset that is not identical to the original set—it contains fewer elements. C is not a subset of A , since C contains an element, 3, that is not contained in A. There are many possible answers here. One would be the set of plays by Shakespeare. This is also a subset of the set of all plays ever written. It is also a subset of all British literature.

Commonly sets interact. For example, you and a new roommate decide to have a house party, and you both invite your circle of friends.

At this party, two sets are being combined, though it might turn out that there are some friends that were in both sets. The union of two sets contains all the elements contained in either set or both sets. The intersection of two sets contains only the elements that are in both sets.

The complement of a set A contains everything that is not in the set A. Notice that in the example above, it would be hard to just ask for A c , since everything from the color fuchsia to puppies and peanut butter are included in the complement of the set. For this reason, complements are usually only used with intersections, or when we have a universal set in place.

A universal set is a set that contains all the elements we are interested in. This would have to be defined by the context. Grouping symbols can be used like they are with arithmetic — to force an order of operations. These illustrations now called Venn Diagrams. A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets.

A c will contain all elements not in the set A. The elements in the outlined set are in sets H and F , but are not in set W. Often times we are interested in the number of items in a set or subset.

This is called the cardinality of the set. Sometimes we may be interested in the cardinality of the union or intersection of sets, but not know the actual elements of each set. This is common in surveying.

Suppose 20 report tea only, 80 report coffee only, 40 report both. How many people drink tea in the morning? How many people drink neither tea or coffee? This question can most easily be answered by creating a Venn diagram.

We can see that we can find the people who drink tea by adding those who drink only tea to those who drink both: 60 people. We can also see that those who drink neither are those not contained in the any of the three other groupings, so we can count those by subtracting from the cardinality of the universal set, How many people have used neither Twitter or Facebook?

Let T be the set of all people who have used Twitter, and F be the set of all people who have used Facebook. In symbols,. Notice that the first property can also be written in an equivalent form by solving for the cardinality of the intersection:. Fifty students were surveyed, and asked if they were taking a social science SS , humanities HM or a natural science NS course the next quarter.

It might help to look at a Venn diagram. Now, we know that 21 students were taking a SS course. This includes students from regions a, b, d, and e. Privacy Policy. Skip to main content. Module 1: Basic of Set. Search for:. Set Theory It is natural for us to classify items into groups, or sets, and consider how those sets overlap with each other. Basics An art collector might own a collection of paintings, while a music lover might keep a collection of CDs.

Set A set is a collection of distinct objects, called elements of the set A set can be defined by describing the contents, or by listing the elements of the set, enclosed in curly brackets. Notation Commonly, we will use a variable to represent a set, to make it easier to refer to that set later. Subset A subset of a set A is another set that contains only elements from the set A , but may not contain all the elements of A. What is a larger set this might be a subset of?

Union, Intersection, and Complement The union of two sets contains all the elements contained in either set or both sets. Universal Set A universal set is a set that contains all the elements we are interested in. Example 6 If we were discussing searching for books, the universal set might be all the books in the library. If we were grouping your Facebook friends, the universal set would be all your Facebook friends. If you were working with sets of numbers, the universal set might be all whole numbers, all integers, or all real numbers.

Venn Diagram A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Example 11 Create an expression to represent the outlined part of the Venn diagram shown. Try It Now Create an expression to represent the outlined portion of the Venn diagram shown. Cardinality The number of elements in a set is the cardinality of that set.

The cardinality of the set A is often notated as A or n A. What is the cardinality of B? Answers The cardinality of B is 4, since there are 4 elements in the set. Answers The cardinality of this set is 12, since there are 12 months in the year. Answers This question can most easily be answered by creating a Venn diagram. Answers Let T be the set of all people who have used Twitter, and F be the set of all people who have used Facebook. Example 16 Fifty students were surveyed, and asked if they were taking a social science SS , humanities HM or a natural science NS course the next quarter.

## Venn diagram

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. Venn Diagram: Union of 2 Sets. Venn Diagram: Intersection of 2 Sets.

Let us discuss the important operations here: The important operations on sets are. Set operations in LINQ refer to query operations that produce a result set that is based on the presence or absence of equivalent elements within the same or separate collections or sets. For any one of the set operations, we can expand to set builder notation, and then use the logical equivalences to manipulate the conditions. Since we're doing the same manipulations, we ended up with the same tables. Create a Venn diagram to show the relationship among the sets. Fuzzy set operations are a generalization of crisp set operations, each of which is a fuzzy set operation. The standard query operator methods that perform set operations are listed in the following section.

To the extent only that those set operations like except are simulated with things like left join where rhs. This venn diagram shows all the possible relationships for records in a database with respect to two sets. C d 4 10 8 6 1 2 7 3 5 9 a number is chosen at random from those shown on the venn. While solving, pay careful attention to phrases like and, or. These pdf worksheets contain venn diagrams without universal set.

Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. Sets and the Universal Set.

## Set operations and venn diagrams pdf merge

A Venn diagram is a widely-used diagram style that shows the logical relation between sets , popularised by John Venn in the s. The diagrams are used to teach elementary set theory , and to illustrate simple set relationships in probability , logic , statistics , linguistics and computer science. A Venn diagram uses closed curves drawn on a plane to represent sets. Very often, these curves are circles or ellipses. Similar ideas had been proposed before Venn.

Sets are treated as mathematical objects. Similarly to numbers, we can perform certain mathematical operations on sets. Below we consider the principal operations involving the intersection , union , difference , symmetric difference , and the complement of sets.

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.

### 5.3: Properties of Set Operations

Some of the properties of set operations are closely related to some of the logical operators we studied in Section 2. This is due to the fact that set intersection is defined using a conjunction and , and set union is defined using a disjunction or. Explain why each of the following statements is true. This section contains many results concerning the properties of the set operations.

Нам нужно поговорить. Если Грег Хейл ворвется… - Он не закончил фразу. Сьюзан потеряла дар речи. Он пристально посмотрел на нее и постучал ладонью по сиденью соседнего стула.

Venn Diagrams. ▫ A Venn diagram is a technique used for picturing set relationships. ▫ A rectangle usually represents the universal set,. U. ❑ The items inside.

#### Set Theory

Джабба, мне не до шуток. - Ну хорошо, - сказал он, приподнимаясь на локтях.  - Может быть, у них закоротило генератор. Как только освобожусь, загляну в шифровалку и… - А что с аварийным питанием. Если закоротило генератор, почему оно не включилось. - Не знаю. Может быть, Стратмор прогоняет что-то в ТРАНСТЕКСТЕ и на это ушло все аварийное питание.

Это наш долг. Нравится нам это или нет, но демократию от анархии отделяет не очень-то прочная дверь, и АНБ ее охраняет. Хейл задумчиво кивнул: - Quis custodiet ipsos custodes. Сьюзан была озадачена. - Это по-латыни, - объяснил Хейл.  - Из сатир Ювенала.

Quien es. Кто он. - Понятия не имею. - Похож на китайца. Японец, подумал Беккер. - Бедняга.

Вернувшись в лабораторию, Чатрукьян никак не мог решить, должен ли он идти домой. Неисправность ТРАНСТЕКСТА угрожала и базе данных, а легкомыслие Стратмора не имело оправданий.

Халохот ликвидировал его с помощью НТП - непроникающей травматической пули. Это резиновая капсула, которая при попадании растворяется. Все тихо и чисто. Перед сердечным приступом мистер Танкадо не почувствовал ничего, кроме легкого укола.

Нужно было думать о долге - о стране и о чести. Стратмор полагал, что у него еще есть время. Он мог отключить ТРАНСТЕКСТ, мог, используя кольцо, спасти драгоценную базу данных. Да, подумал он, время еще .