Types of sets

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TYPES OF SETS

1.Empty Set or Null Set

If the set has no element then it is said to be empty set. The empty set is also called as void set or null set.
It is denoted by Ø or { }.For example, 
  • The set of all integers between 1 and 2
  • The set of 30 days in the month of February 

2.Singleton Set

If the set has only one element then it is said to be singleton set. For example,
  • The set of all even prime numbers
  • The set of all direction of sun rise

Cardinal number of a set : When a set is finite, it is very useful to know how many elements it has. The number of elements in a set is called the Cardinal number of the set. The cardinal number of a set A is denoted by n(A)


3.Finite Set

A set with limited number of elements or possible to list is called a finite set. For example,
  • Limited number of students in a class
    The set of months in a year
  • The set of whole numbers from 0 to 100



4.Infinite Set

THE VALUE OF PI
 A set which is not limited and impossible to list  is called an infinite set. 
For example,
  • The set of all whole numbers
  • The set of all even numbers


5.Equivalent Sets

If two finite sets A and B contains same number of elements then it is said to be an equivalent set. It is written as A ≈ B. For example, 
  • A = { India, Tamil Nadu } and B = { Country, State }
  • P = { Mathematics and Science } and Q = { History and Geography }
2 Apples, 2 Bananas, 2 Guavas
Here the both the examples has same number of elements 
i.e. n = 2. 
We can write it as n(A) = 2 = n(B)  and n(P) = 2 = n(Q)





Each set has exactly same
number of days 
6. Equal Sets

If two sets contain exactly the same elements then 
it is said to be an equal sets. For example,
  • A = { a, e, i, o, u } and B = { i, e, u, o, a }
  • X = {football, soccer} and Y ={soccer, football}



7. Universal Set

Shopping Mall
A Universal set is a set which contains all the elements of all the sets under consideration and is usually denoted by U. 
For example,
  • The set of solar system
  • The set of school bags

8.Subset

Let A and B be two sets. If every element of A is also an element of B, then A is called a subset of B. We write A ⊆ B.   A ⊆ B is read as “A is a subset of B” 
 Thus A ⊆ B, if a ∈ A implies a ∈  B. For examples, 
  • Solar system contains planets

    {1}⊆{1,2,3} 
  • {2} ⊆{1,2,3}


9.Proper Subset

Let A and B be two sets. If A is a subset of B and A≠B, then A is called a proper subset of B and we write A ⊂ B. For example, 
  • If A={1,2,5} and B={1,2,3,4,5} then A is a proper subset of B i.e. A ⊂ B.
  • E = { a, u, e } and F = { a, e, i, o, u }



10.Disjoint Sets

If two sets A and B do not have common elements then it is said to be a disjoint sets. In other words, if A∩B=∅, then A and B are said to be disjoint sets.
For example, 
  • A = {yellow, blue, white} ≠ B = {green, red, black}
  • C = {2,4,6} ≠  D = {1, 3, 5}