Types of Sets

1.       Empty  set :- A set having no element is called empty set . It is denoted by φ(Phi) or { } e.g. A set of all students of eleventh class in a high school is an empty set because no student of a high school is in class eleventh we can write it as

                                         E = { x:x is a student of class eleventh in a high school}

                     or               E = { } = φ

    An empty set is also called null set or void set .

2 Singleton set :- A set containing only one element is called singleton set e.g The set of all whole numbers which are not natural numbers, this set contains only one element. We can write it as

                                     B = {x:x is a whole number but x is not a natural number}

                          or       B = {0}

3 Finte set:- A set which is either empty or contains  a definite numbers of elements is called finite set . The sets E and B discussed above are finite sets, let us take one more example of finite set. Take a set ‘C’ of natural numbers less than 10

                                     C  = {x:x is a natural number less than 10}

                      or           C = {1,2,3,4,5,6,7,8,9}

4 Infinite set :- A  set which is not finite is called infinite set . All the elements of an infinite set cannot be listed in roster form

e.g  Set of all natural numbers i.e.    N = {x:x is a natural number}

                                                                 N = {1,2,3,…}