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.

## Set Theory > Basic Set Theory (Stanford Encyclopedia of Philosophy)

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.

## Set theory

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. Skip to main content.

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### Set Theory Quiz: Solve these problems for practice

How the operations are carried out in union of sets and intersection of sets? Union of Sets : Definition of union of sets with examples. Learn how to find the union of two sets and worked-out examples. Problems on Union of Sets : Learn how to find the union of two or more sets and worked-out examples of operations on union of sets. Intersection of Sets : Definition of intersection of sets with examples. Learn how to find the intersection of two sets and worked-out examples.

Problems on Intersection of Sets : Learn how to find the intersection of two or more sets and worked-out examples of operations on intersection of sets. Difference of two Sets : Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set : Definition of complement of a set and their properties with some worked-out examples. Problems on Complement of a Set : Learn how to find the complement of two or more sets and worked-out examples of operations on complement of sets. Problems on Operation on Sets : Learn how to find the union and intersection of two or more sets and worked-out examples of the two basic operations of sets. Cardinal number of a set : Definition of a cardinal number of a set, the symbol used for showing the cardinal number, worked-out examples. Cardinal Properties of Sets : Learn how to solve the real-life word problems on set using the cardinal properties.

Relationship in Sets using Venn Diagram : Learn how to find the relationship of the union, intersection and difference of the two sets using Venn-diagram. Disjoint of Sets using Venn Diagram : Learn how to represent the disjoint sets of union and intersection using Venn-Diagram.

Examples on Venn Diagram : Learn how to use the basic concepts of sets for solving the different types of problems on Venn diagram. Laws of Algebra of Sets : Here we will discuss about some fundamental laws of algebra of sets. Properties of Elements in Sets : Learn all the important properties of elements in sets. Reflexive Relation on Set : What is reflexive relation on set? Learn step-by step to get the reflexive relation in the basic concepts of sets using solved examples.

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Learn step-by step using solved examples. Transitive Relation on Set : What is transitive relation on set? Learn step-by step to get the equivalence relation in the basic concepts of sets using solved examples. Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need. Worksheet on Set. Worksheet on Set Theory. Worksheet on Elements Form a Set.

## Basic Concepts of Sets

Worksheet on Elements of a Set. Worksheet to Find the Elements of Sets. Worksheet on Properties of a Set. Worksheet on Sets in Roster Form. Worksheet on Sets in Set-builder Form. Worksheet on Representation on Set.

Worksheet on Finite and Infinite Sets. Worksheet on Equal Sets and Equivalent Sets. Worksheet on Empty Sets. Worksheet on Subsets. Worksheet on Union and Intersection of Sets. Worksheet on Disjoint Sets and Overlapping Sets. Worksheet on Difference of Two Sets.

Worksheet on Set Operations.