SETS :Types of sets and equal sets

Types of sets

Singleton Set :
Defination :A set consisting of a single element is called a singleton set. 
Example   :A = {2} A is the set of even prime numbers .

Empty Set or Null Set:
 Defination :If there is not a single element in the set which satisfies the given condition then it is called a Null set or an empty set.

Null set is represented by { } or a symbol ∅ (phi).
Example  :B = {x | x is natural number between 2 and 3.}      ∴ B = { } or ∅.

Finite Set :
 Defination :If a set is a null set or number of elements are limited and countable then it is called as ‘Finite set’.
Example  :C = {p | p is a number from 1 to 22 divisible by 4.}

 ∴ C = {4, 8, 12, 16, 20}.

Infinite Set :
If number of elements in a set is unlimited and uncountable then the set is called ‘Infinite set’.

Example  :N = {1, 2, 3, . . . }.

Remember this !

N, W, I, Q, R all these sets are infinite sets.

Equal sets:

Two sets A and B are said to be equal, if every element of set A is in set B and every element of set B is in set A.

'Set A and set B are equal sets', symbolically it is written as A = B.

Ex (1): A = { x | x is a letter of the word ‘listen’.}
           ∴ A = { l, i, s, t, e, n}

              B = { y | y is a letter of the word ‘silent’.}             ∴ B = { s, i, l, e, n, t}

Though the elements of set A and B are not in the same order but all the elements are identical.

∴ A = B

Ex (2):     A = {x | x = 2n , n ϵ N, 0 < x ≤ 10},                       ∴ A = {2, 4, 6, 8, 10}

               B = { y | y is an even number, 1≤ y ≤ 10},              ∴ B = {2, 4, 6, 8, 10}

∴ A and B are equal sets.

Now think of the following sets.

C = {1, 3, 5, 7} D = { 2, 3, 5, 7}

Are C and D equal sets ? Obviously ‘No’

Because 1 ϵ C, 1 ∉ D, 2 ϵ D, 2 ∉ C

∴ C and D are not equal sets. It is written as C ≠ D

Ex (3) If A = {1, 2, 3} and B = { 1, 2, 3, 4}then     A ≠ B verify it.

Ex (4) A = {x | x is prime number and 10 < x < 20} and B = {11, 13, 17, 19}

Here A = B. Verify,