Set

Set:

A set is a collection of well defined and well-distinguished objects.

For example: the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}.

There are two ways of describing a set 

i    Extension  or Tabular or Listing or Roster Method

ii.   In-tension or Selector or set-builder or rule method

Extension or Tabular Method:

Every object are listed that falls under the definition  of the concept in question.

Example:

a)    A set of vowels : A ={a,e,i,o,u}

b)    A set of odd numbers: A = {1, 3, 5, 9, …}

In-tension or Selector or builder method:

The elements are not listed but are indicated by description of there characteristics.

Examples:

a)    A= {x : x is a vowels in English alphabet}

b)    B= { x : x is a odd natural number}

Types of set:

Finite set:

A finite set is a set that has a finite number of elements.

For example:  A = {1, 2, 3, 4}

Infinite set:

An infinite set is a set that has a infinite number of elements.

For example:

a)    A = {1, 2, 3, …..}

b)    the set of all integers, {..., -1, 0, 1, 2, ...}, is a countably infinite set;

c)    the set of all real numbers is an uncountably infinite set.

Empty, Null or Void set:

The empty set is the unique set that having no elements

Example:

a)    The number of rivers in Dhaka city :  A = { },

Unit set:

A set with exactly one element.

Example:

a)    The number of currency in Bangladesh

A= { Taka }

Equal set:

Two sets A and B are said to be equal if every element of A is also an element of B and every element of B is also an element of A.

i. e.  A=B if and only if { x∈A  and  x∈B}

Example: A ={1,2,3,}, B={3,2,1}

Equivalent Set:

If the elements of one set can be put into one to one correspondence with the elements of another set, then the two sets are called equivalent sets.

Example: A = {a,b,c,d,e}  and B= {1,2,3.,4,5}, thus

a        b        c        d        e

1        2        3        4        5

Subset:

If every element of a set A is also an element of the set B, then A is called the subset of B. It is denoted by A ⊆ B .

Example: A= {1,2,}  B = {1,2,3,4} than A ⊆ B 

Proper subset:

If all the element of a set A are the elements of the set B, but all the element of a set B are  not the elements of the set A, then A is called the proper subset of B. . It is denoted by A ⊂ B.

Example: A= {1,2,}  B = {1,2,3,4} than A ⊂ B