Mathematics: Relations Functions Sets: Classification of Sets: Finite and Infinite Sets, Empty Set

Get top class preparation for UGC right from your home: Get complete video lectures from top expert with unlimited validity: cover entire syllabus, expected topics, in full detail- anytime and anywhere & ask your doubts to top experts.

Download PDF of This Page (Size: 168K)

Classification of Sets

Classification of Sets

Classification of Sets

Classification of Sets

Finite and Infinite Sets

A set is said to be finite if its elements can be counted and it is said to be infinite if it is not possible to count up to its last element.

Example:

Let and be two sets where

Solution:

  • As it is clear that the number of elements in set is not finite while number of elements in set is finite. is said to be an infinite set and is said to be a finite set.

Empty (Null) Set

A set which has no element is said to be a null/empty/void set, and is denoted by or.

Example:

Consider the following sets.

Solution:

  • Set consists of real numbers but there is no real number whose square is. Therefore, this set consists of no element.

  • Similarly, there is no such number which is less than and greater than. Such a set is said to be a null (empty) set. It is denoted by the symbol or.

Singleton Set

A set which has only one element is known as singleton.

Example:

Consider the following set:

Solution:

  • As there is only one even prime number namely, so set will have only one element. Such a set is said to be singleton. Here

Equal and Equivalent Sets

Two sets and are said to be equivalent sets if they have same number of elements but they are said to be equal if they have not only the same number of elements, but elements are also the same.

Example:

Consider the following example.

(I) (II)

Solution:

  • In example (I) Sets and have the same elements. Such sets are said to be equal sets and it is written as.

  • In example (II) sets and have the same number of elements but elements are different. Such sets are said to be equivalent sets and are written as.

Disjoint Sets

Two sets are said to be disjoint if they do not have any common element.

Example:

Given that and Are and disjoint sets?

Solution:

  • If we solve , we get

  • and

  • Clearly, and are disjoint sets as they do not have any common element.

Developed by: