The below given is the Basic sets concepts tutorial which contains the definition and basic concepts of sets. All the basic concepts are explained in a understanding manner with the help of examples. Make use of this set operations tutorial to get an idea on sets.

A set is a collection of well-defined objects. This means that the objects of a set are all distinct, i.e., no two objects are the same.
Generally, sets are named with the capital letters A, B, C, etc. The elements of a set are denoted by the small letters a, b, c, etc.
**Reading notation**
If x is an element of the set A, we write x ∈ A.
If x is not an element of the set A, we write x ∉ A.
**Example:**
Consider the set **A = { 4, 8, 5, 9 }**
If 4 is an element of A, it should be written as **4 ∈ A.**
If 7 is not an element of A, it should be written as **7 ∉ A.**
**Representation of a set**
A set can be represented in any one of the following three ways or forms.
(i) Descriptive form
(ii) Set-builder form or Rule form
(iii) Roster form or Tabular form
**Descriptive Form**
One way to specify a set is to give a verbal description of its elements. It is called as the descriptive form of specification.
**Example:**
(i) The set of all natural numbers.
(ii) The set of all prime numbers less than 100.
(iii) The set of all letters in English alphabets.
** Set-Builder Form or Rule Form**
Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.
**Example**
A = { x : x is a letter in the English alphabet }
**Roster Form or Tabular Form**
Listing the elements of a set inside a pair of braces { } is called the roster form.
**Example**
Let Q be the set of even natural numbers less than 15.
In roster form we write Q = { 2, 4, 6, 8, 10,12,14 }
**Note:**
(i) In roster form each element of the set must be listed exactly once. By convention, the elements in a set should not be repeated.
(ii) Let A be the set of letters in the word “coffee”,
That is, A = { t, r, u, e }. So, in roster form of the set A the following are invalid.
{ t, r, e } -------> (not all elements are listed)
{ t, r, u, u, e } -------> (element ‘f’ is listed twice)
(iii) In a roster form the elements in a set can be written in any order.
The following are valid roster form of the set containing the elements 2, 3 and 4.
{ 2, 3, 4 }
{ 2, 4, 3 }
{4, 3, 2 }
Each of them represents the same set.
(iv) If there are either infinitely many elements or a large finite number of elements, then three consecutive dots called ellipsis are used to indicate that the pattern of the listed elements continues, as in { 5, 6, 7,...... } or { 3, 6, 9, 12, 15,........60 }.
(v) Ellipsis can be used only if enough information has been given so that one can figure out the entire pattern.