Concepts of Sets
We often have to deal with the collection of objects. A single word is used to denote a collection such as
1. A BUNCH of Keys
2. A CLASS of students
3. An ALBUM of photograph
In mathematics, we too deal with collections and we use the word “SET” to describe a well-defined collection of objects.
Definition: A well-defined collection of distinct objects is called a SET.
Sets are usually denoted by capital letters of the alphabet like A, B, C, etc. The objects of collections are called the ELEMENTS or MEMBERS of the set and are denoted by a, b, c, x, y, z, etc.
Representation of Set
A set can be represented in many ways such as:
Description form
Roster or Tabular form
Set-Builder or Rule Form
In Description Form a well-defined description of the set is given e.g., N is the set natural numbers.
In roster or tabular form all the elements of a set are actually written down, separated by commas and enclosed within braces, e.g., N={1,2,3,4,5, …}
In set-builder or rule form we state the requirements that any object must in order to be a member of the set.
Cardinal Number
The number of members in a set A is the cardinal number of the set. It is denoted by n(A), read as ‘the number of elements in the set A.
Equal Sets
Two sets are said to be equal if they have the same elements.
Equivalent Sets
Two sets are said to be equivalent if they have an equal number of elements in them the cardinal numbers of both the sets must be equal
Disjoint Sets
Two sets are said to be disjoint if they have no elements in common.
Finite Set
A finite set has elements that can be counted with the counting process coming to an end e.g. The set o students in your class
Infinite Set
A set in which the counting of its elements does not come to an end e.g. The set of all-natural numbers
Empty Set or Null Set or Void Set
A set having no elements is called an empty set. It is denoted by pronounced as ‘phi’ or by {}.
Overlapping Sets
If two sets A and B have some elements in common then they are called overlapping sets.