class : 11 Science
name : Khushwant SETS Mathematics project

Slide 3:

contents History of sets
Sets
Sets representation
Types of set
History of Venn
Union of sets
Intersection of set
Complements of set

Slide 4:

HISTORY OF SETS The theory of sets was developed by
German mathematician Georg Cantor
(1845-1918) . He first encountered sets while working on “ Problems on
Trigonometric series”. SETS are being
Used in solving mathematics problems since they were discovered .

Slide 5:

sets Collection of object of a particular
kind, such as, a pack of cards, a
crowed of peoples, a cricket team, etc, In mathematics of natural no.,
points, prime no., etc.
A set is a well defined collection of
object.

Slide 6:

Elements of a set are synonymous terms.
Sets are usually denoted by capital letters.
Elements of a set are represented by small
letters. a set is a well defined collection
of object.

Slide 7:

sets representation There are two ways to represent sets :
Roster or tabular form .
Set-builder form .

Slide 8:

set-builder form In set-builder form, all the elements of a set possess a single common property which is not possessed by any element
outside the set .
e.g. :
set of natural numbers k .
k= { x : x is a natural no }

Slide 9:

roster form In roster form all the elements of sets are listed, the elements are being
separated by commas & are enclosed
within braces { } .
e.g. :
set of 1,2,3,4,5,6,7,8,9,10 .
{ 1,,2,3,4,5,6,7,8,9,10 }

Slide 10:

examples of sets in maths

Slide 11:

types of sets Empty set.
Finite & Infinite sets.
Equal sets.
Subset.
Power set.
Universal set.

Slide 12:

the empty set A set which doesn’t contains any element
is called the empty set or null set or void set, donated by symbol f or { } .
e.g. : let R = { x : 1 < x < 2, x is a natural
number }

Slide 13:

finite & infinite sets A set which is, empty or consist of a definite no. of elements is called finite otherwise, the set called infinite .
e.g. : let k be the set of the days of the week .
Then k is finite. (finite)
let r be the set of points on a line.
Then R is infinite. (infinite)

Slide 14:

equal sets Two sets k & R are said to be equal if they have exactly the same elements and we write k=R . Otherwise, the sets are said to be unequal and we write k?R.
e.g. :
let k = { 1,2,3,4,} & R= { 1,2,3,4 }.
then k=R

Slide 15:

subsets

Slide 16:

power set The set of all the subsets of a given set is called power set of that set.
The collection of all subsets of a set k
is called the power set of k denoted by
P ( k ) . In P ( k ) every element is a set.
if k = { 1,2 }
P ( k ) = { f , { 1 } , { 2 } , { 1 , 2 } }

Slide 17:

universal set The super set of all the given type of sets would be called as universal set
of all the other given type of sets.
e.g. : the set of real numbers would be the
universal set of all the other sets
of numbers.
Note : [excluding negative roots]

Slide 18:

Subsets of r The set of natural no. N={ 1,2,3, …}
The set of integers Z={… , -2,-1,0,1,2,…}
The set of rational no. Q={ x : x = p/q ,
p,q are integers and q ? 0 }
Note : members of Q also include negative
numbers.

Slide 19:

Intervals of subsets of r The interval denoted as ( a , b ) , a & b are Real numbers ; is an open interval , means including all the elements between a to b but excluding a & b .

Slide 20:

The interval donated as [ a , b ] , a & b are Real numbers ; is an closed interval , means including all the elements between a to b &including a & b.

Slide 21:

types of intervals ( a , b ) = { x : a < x < b }
[ a , b ] = { x : a = x = b }
[ a , b ) = { x : a = x < b }
( a , b ] = { x : a < x = b }

Slide 22:

history of Venn diagrams Most of the relationships of sets can be represented using Venn diagrams . Venn are named after the English logician, Johan Venn
(1834-1883).

Slide 23:

Venn consist of rectangles & closed cure usually circles. The universal set is represented usually by rectangle & its subsets by circle.

Slide 24:

illustration 1. In fig 1., U =
{ 1, 2, 3, …, 10 } is the universal set of which
A = { 2, 4, 6, 8, 10 } is a subset.

Slide 26:

Union of sets : The union of two sets A & B is the set C which consists of all those elements which are either in A or B or in both.

Slide 27:

some properties of union

Slide 28:

intersection of sets : The
intersection of two sets A & B is the set of all those elements which belong to both A & B.

Slide 29:

some properties of intersection :

Slide 30:

complements of sets : Let U = { 1, 2, 3, 4, …, 10 } & A = { 1, 2, 3 }
Now the set of all those elements of U
which doesn‘t belongs to A will be called
as A’ or A complement.

Slide 31:

properties of complements of sets :

Slide 32:

Laws of double complementation :
( A’ )’ = A
Laws of empty set and universal set :
f’ = U & U’ = f THE END

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.

By: anitapandey (44 month(s) ago)

excellent work