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

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