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The four important set operations that are widely used are: Union of sets; Intersection of sets; Complement of sets; Difference of sets; Fundamental Properties of Set operations: Like addition and multiplication operation in algebra, the operations such as union and intersection in set theory obeys the properties of associativity and commutativity.
- Union of Sets
The union of set A and set B is equal to the set containing...
- Intersection of Sets
Consider a set A consisting of the prime numbers less than...
- Height Of Equilateral Triangle
The main application use of altitude is that it is used for...
- Mutually Exclusive Events
A clear case is the set of results of a single coin toss,...
- Union of Sets
- Writing a Set Using the Roster or Listing Method. Write a set consisting of your three favorite sports and label it with a capital SS. Answer. There are multiple possible answers depending on what your three favorite sports are, but any answer must list three different sports separated by commas, such as the following
- Identifying Well-Defined Sets. For each of the following collections, determine if it represents a well-defined set. The group of all past vice presidents of the United States.
- Representing the Empty Set Symbolically. Represent each of the following sets symbolically. The set of prime numbers less than 2. The set of birds that are also mammals.
- Writing a Finite Set Using the Roster Method and an Ellipsis. Write the set of even natural numbers including and between 2 and 100, and label it with a capital EE.
- Set Theory Definition
- History of Set Theory
- Examples of Sets
- Important Terms Related to Set Theory
- Types of Sets
- Set Theory Symbols
- Set Theory Formulas
- De Morgan’s Laws
- Visual Representation of Sets Using Venn Diagram
- Conclusion – Set Theory
Sets are defined as ”a well-defined collection of objects”. Let’s say we have a set of Natural Numbersthen it will have all the natural numbers as its members and the collection of the numbers is well defined that they are natural numbers. Note: A set is always denoted by a capital letter. A set of Natural Numbers is given by: The above example is ...
The concept of Set Theory was propounded in the year 1874 by Georg Cantorin his paper name ‘On a Property of Collection of All Real Algebraic Numbers‘. His concept of Set Theory was later used by other mathematicians in giving various other theories such as Klein’s Encyclopedia and Russell Paradox. Sets Theory is a foundation for a better understan...
Some common examples of sets are mentioned below: 1. Set of Natural Numbers: N = {1, 2, 3, 4….} 2. Set of Even Numbers: E = {2, 4, 6, 8…} 3. Set of Prime Numbers: P = {2, 3, 5, 7,….} 4. Set of Integers: Z = {…, -4, -3, -2, -1, 0, 1, 2,….}
Some of the important terms related to sets are mentioned below. These terms will be used several times in this article, and knowing these terms will help you learn set theory.
There are different types of sets categorized on various parameters. Some types of sets are mentioned below:
Various symbols are used in Sets Theory. The notations and their explanation are tabulated below: Read More: Set Theory Symbols.
The set theory formulasare given for two sets – overlapping and disjoint sets. Let’s learn them separately
De Morgan’s Lawis applicable in relating the union and intersection of two sets via their complements. There are two laws under De Morgan’s Law. Let’s learn them briefly
Venn Diagramis a technique for representing the relation between two sets with the help of circles, generally intersecting. For Example: Two circles intersecting with each other with the common area merged into them represent the union of sets, and two intersecting circles with a common area highlighted represent the intersection of sets while two ...
We have covered all the concepts required to learn the set theory. We have covered the history, definition, examples, symbols, operations, and formulas of set theory. Set theory is an important topic and many questions come from set theory in many competitive Exams. Students should focus on set theory and practice with some questions provided in th...
- 10 min
Jan 24, 2021 · The roster method lists all the elements or members in the set, whereas a description in words explains what elements are in the set using a sentence. And set-builder notation expresses how elements are given membership in the set by specifying the properties that define the collection of objects.
When describing a set, It is not necessary to list every element in that set. Thus, there are two methods for indicating a set of objects: 1) listing the elements and 2) describing the elements. We will distinguish between these two methods in examples 10 and 11 below.
A set is a collection of objects (without repetitions). To describe a set, either list all its elements explicitly, or use a descriptive method. Intervals are sets of real numbers. The elements in a set can be any type of object, including sets. We can even have a set containing dissimilar elements.
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Methods to write a set. (i) Roster Method : In this method a set is described by listing elements, separated by comma and enclose then by curly brackets. Example : The set of vowels of English Alphabet may be described as {a, e, i, o ,u}. (ii) Set builder Form :
