Basic Concepts of Set Symbols
Various ideas are covered at various levels of schooling in set theory. Set representation, set types, set operations (such as union and intersection), set cardinality and relations, and so on are among the essential concepts. Some of the essential concepts in set theory are as follows:
Universal Set
The capital letter ‘U’ is commonly used to represent a Universal Set. It is also occasionally symbolized by ε(epsilon). It is a set that contains all the elements of other sets as well as its own.
Complement of Set
The complement of a set comprises all of the universal set’s constituents except the elements of the set under examination. If A is a set, then its complements will contain all of the members of the specified universal set (U) that are not included in A. A set’s complement is indicated or expressed as A’ or Ac and is defined as:
A’= {x ∈ U: x ≠ A}
Read more about Complement of Set.
Set Builder Notation
Set Builder notation is the method to represent sets in such a way that where we don’t need to list all the elements of the set, we just need to specify the rule which is followed by all the elements of the set. Some examples of these notations are:
If A is a collection of real numbers.
A = {x : x ∈ R}
If A is a collection of natural numbers.
A = {x : x > 0 and x ∈ Z]
Where Z is set of Integers.
Read more, Representation of Sets.
Set Symbols
Set Symbols are a collective term used for all the symbols used in set theory which is the branch of mathematics that deals with the collection of objects and their various properties. A set is a well-defined collection of objects where each object in the collection is called an element and each element of the set follows a very specific rule. Generally, capital letter of English alphabets are used to denote sets and some letters denotes some specific sets in set theory.
There are many symbols used throughout the study of this branch of math, some of the common symbols are {}, |, :, ∈, ∉, ⊆, U, Ø, etc. We will discuss all these symbols in detail in the article including the history of these symbols as well. So, let’s start our journey of learning about various different set symbols used in set theory.
Table of Content
- What are Set Symbols?
- History of Set Symbols
- Basic Concepts of Set Symbols
- Set Symbols in Maths
- Set Theory Symbols
- Solved Examples on Set Symbols
- Practise Qusetion for Set Symbols
- FAQs
Contact Us