Representation of set | Roster or Tabular form | Set Builder form

A set is often described in the following two forms. One can make use of any one of these two ways according to his/her convenience 

(i) Roster form or Tabular form
(ii) Set-builder form
Let us now discuss one by one.
(i) Roster form or Tabular form:-
In this form a set is described by listing the elements    and separate by commas, within braces { }
Example
a) The set of Vowels of English Alphabet , may be described by {a, e, i, o, u}.
b) The set of even natural numbers can be described by  {2, 4, 6, 8,….}. Dot is stand for so on
NOTE
a) The order in which elements are written in a set makes no difference. Like set {1, 2, 3, 4} is same as {2, 3, 1, 4}.
b) Repetition of elements of a set also does not have any change. Like set {1, 2, 3} is same as {1, 2, 2, 3}.
(ii) Set builder form
In this form a set is described  by a some definite rules. In such cases a set is described by {x : p(x) holds }. Where p(x) is some definite rule in which elements will be written or p(x) is properties of given set. ” : ” is read as ‘such that’.
{x : p(x) holds} is read as ‘The set of all x such that such that x holds p(x).
Example
a) The set E of all even natural numbers can be written as
E={ x : x ∈ N, x=2n, n ∈ N }
b) The set A={ 1, 2, 3, 4, 5, 6, 7 } can be written as A={ x : x < 8, x ∈ N }