## Set, Relation & Function ,type of sets,

__Set, Relation & Function__

Set is any collection
of distinct and distinguishable objects of our intuition or thought’.

**Following are the some examples of sets:**

**•The collection of vowels in English alphabets, i.e. A = {a, e, i, o, u}.**

**•The collection of all states in the Indian Union.**

**•The collection of all past presidents of the Indian Union etc.The following sets, we will use frequently**

In
this session
and following sessions:

*•N : For the set of natural numbers*

*•Z or I: For the set of integers*

*•Z+ or I+: For the set of all positive integers*

*•Q : For the set of all rational numbers*

*•Q+ : For the set of all positive rational numbers*

*•R : For the set of all real numbers*

*•R+ : For the set of all positive real numbers*

*•C : For the set of all complex numbers*__Representation of a Set__

A set is often
represented in the following two ways:(I)Roster method (Tabular form)

**In this method a set is described by listing**

elements separated by commas, within braces { }.

elements separated by commas, within braces { }.

**For example, the set of even natural numbers can be described as {2, 4, 6, 8, ...}.**

(II)Set Builder Method

*In this method, a set is described by a characterizing property*

*(x) of its element x. In such a case the set is described by {x : P(x) holds} or {x / P(x) holds}*

*The symbol ‘|’ or ‘:’ is read as ‘such that’.In this representation the set of all even natural numbers can be written as : {x / x = 2n for }*
Types of Sets

Empty sets:

**A set having no element is****called an empty set. It is also known as****null set or void set. It is denoted by phi**
Singleton set:

**A set having single element is called singleton set.****For example, {2}, {0}, {5} are singleton set.**
Finite set:

**A set is called a finite set if it is called either void set or its elements can be counted by natural numbers and process**

of listing terminates at a certain natural numbers.of listing terminates at a certain natural numbers.

**For example, {1, 2, 4, 6} is a finite set because it has four elements.**

Infinite set:

*A set which is not a finite set, i.e. the counting up of whose elements is impossible, is called an infinite set.For example:*

*(i)The set of all straight line in a given plane.*

*(ii)The set of all natural numbers.*

*The set of real numbers between ‘1’ and 2*
Equivalent and Equal Sets

Equivalent sets:

*Two finite sets A and B are equivalent if their cardinal number is same, i.e. n(A) = n(B).*
Equal sets:

*Two sets A and B are said to be equal if every element of A is a member of B, and every element of B is a member of A.**For example:*

*A = {4, 5, 6} and*

B = {a, b, c} are equivalent but

B = {a, b, c} are equivalent but

*A = {4, 5, 6} and*

C = {6, 5, 4} are equal, i.e. A = C.

C = {6, 5, 4} are equal, i.e. A = C.

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