Classification of Set

# Types of set :

   • Finite Set

   • Infinite Set

   • Equal Set

   • Equivalent set

   • Singleton set

   • Disjoint Set

# Finite Set :

   A set which is empty or consists of a definite number of elements is called Finite Set.

   e.g : • Let W be the set of the days of the week. Then W is finite set.

            • Let S be the set of solutions of the equation x² – 16 = 0. Then S is finite.

# Infinite Set :

   A set which is non-empty or consists of a infinite number of elements is called Infinite Set.

  e.g :  • Let G be the Set of points on a line. Then G is Infinite Set.

            • B = { x : x is a natural number }

# Equal Set :

   Two Sets A and B are said to equal if they have exactly the same elements and we write A = B .

    Otherwise, the sets are said to be unequal and we write A ≠ B .

  e.g : • Let A = { 1 , 2 , 3 , 4 } and  B = { 3 , 1 , 4 , 2 } . Then A = B.

           • Let A be the set of prime numbers less than 6 and P the set of prime factors of 30 and also these are less                    than 6.   

   Note : A set does not change if one or more elements of the set are repeated.

               e.g :  the sets A = { 1 , 2 , 3 } and B = { 2 , 2 , 1 , 3 , 3 } are equal, since each element  of A is in B and vice-                          versa. That is why we generally do not repeat any element in describing a set.

# Equivalent Set :

   Two sets A and B are said to be Equivalent sets if they have same number of elements.

   e.g :  D = { 1 , 2 , 3 }  and  E = { a , b , c }

   In this above example sets D and E have the same number of elements but elements are different.

# Singleton Set :

   A set which has only one element is known as Singleton Set.

   e.g :  A = { x:x is an even prime number } or A = { 2 }

# Disjoint Set :

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

     e.g :  sets A = { 1 , 3 , 5 } and B = { 2 , 4 , 6 } are disjoint sets.