Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {},  for example, A = {1,2,3,4} is a set. 

Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is represented by a capital letter. The number of elements in the finite set is known as the cardinal number of a set.

Definition of Sets

Let us take an example: A = {1, 2, 3, 4, 5 } Since a set is usually represented by the capital letter.  Thus, A is the set and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but cannot be repeated. All the set elements are represented in small letter in case of alphabets.  Also, we can write it as 1 ∈ A, 2 ∈ A etc. The cardinal number of the set is 5.

What are the Elements of a Set

Some commonly used sets are as follows:  – N: Set of all natural number – Z: Set of all integer – Q: Set of all rational number – R: Set of all real number – Z+: Set of all positive integer

What are the Elements of a Set

The order of a set defines the number of elements a set is having. It describes the size of a set. The order of set is also known as the cardinality The size of set whether it is is a finite set or an infinite set, said to be set of finite order or infinite order, respectively.

Order of Sets

The sets are represented in curly braces, {}. For example, {2,3,4} or {a,b,c} or {Bat, Ball, Wickets}. The elements in the sets are depicted in either the Statement form, Roster Form or Set Builder Form. Statement Form In statement form, the well-defined descriptions of a member of a set are written and enclosed in the curly brackets. For example, the set of even numbers less than 15. In statement form, it can be written as {even numbers less than 15}.

Representation of Sets

Roster Form In Roster form, all the elements of a set are listed. For example, the set of natural numbers less than 5. Natural Number = 1, 2, 3, 4, 5, 6, 7, 8,………. Natural Number less than 5 = 1, 2, 3, 4 Therefore, the set is N = { 1, 2, 3, 4 }

Set Builder Form The general form is, A = { x : property } Example: Write the following sets in set builder form: A={2, 4, 6, 8} Solution: 2 = 2 x 1 4 = 2 x 2 6 = 2 x 3 8 = 2 x 4 So, the set builder form is A = {x: x=2n, n ∈ N and 1  ≤ n ≤ 4} Also, Venn Diagrams are the simple and best way for visualized representation of sets.

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