Saturday, June 23, 2012

Classic Treat Free Article Directory ? Set Theory: Types of Sets and ...

Set Theory:
A branch of mathematics which deals with the properties of well defined collection of objects (Sets) is called the Set Theory
A set is a collection of well defined objects in the domain D.
The Universal Set U contains every element in D and the null set contains no element.
Types of Sets:
Finite sets: The sets which have finite number of members or elements are called finite sets.
Example: {set of natural numbers less than 10}={1,2,3,4,5,6,7,8,9}
Infinite sets: The sets which have infinite number of members or elements are called infinite sets.
Example:{set of all natural numbers} = {1,2,3,4??} (the list goes on)
Null or Empty sets: The sets in which there are no members or elements
Example: {set of squares with 6 sides}
Union of Sets:
The union of two sets, set A and set B is the set formed which contains all the elements of set A and also
set B. It is denoted by the symbol ?U?, A U B and read as ?A union B?

Example: Set A={ orange, yellow, green}
Set B={ pink, red, blue}

A U B = {orange, yellow, green, pink, red, blue} (all the elements of set A and set B)

Intersection of Sets:

The Intersection of two sets, set A and set B is the set formed by considering the elements which are common to both the sets A and B. It is denoted by , A B and read as ?A intersection B?

Example: Set A ={orange, yellow, green, pink, red}
Set B= {pink, red, blue, orange}

A B= {orange, pink, red} (elements common to both the sets A and B}

Complement of Sets:

Universal set is the set formed by considering all the elements.

Complement of set A is the set which consists of all the elements of the universal set that are not in set A. It is denoted as A?

Example: Universal set, U ={-1,-2,0,1,2}

Set A={ -1,1}

Set A? = {-2,0,2}
Note: When we combine all the elements of Set A and Set A? we get the Universal set

Know more about the Complement of Sets, online tutoring,Types of Sets
,Set theory. Online tutoring will help us to learn and do our homework very easily without going here and there.

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