PPT: Sets | Mathematics (Maths) Class 11 - Commerce PDF Download

 Page 1


Sets
Page 2


Sets
I n t r o d u c t i o n
Sets are fundamental to modern mathematics, used across virtually all branches. They provide the 
foundation for relations, functions, geometry, sequences, probability, and many other mathematical 
concepts.
German mathematician Georg Cantor (1845-1918) developed set theory while researching trigonometric 
series. This presentation explores basic set definitions and operations.
F o u n d a t i o n
Sets form the basis for 
mathematical relationships and 
structures.
A p p l i c a t i o n s
Used in geometry, probability, 
and throughout mathematics.
O r i g i n
Developed by Georg Cantor in 
the 19th century.
Page 3


Sets
I n t r o d u c t i o n
Sets are fundamental to modern mathematics, used across virtually all branches. They provide the 
foundation for relations, functions, geometry, sequences, probability, and many other mathematical 
concepts.
German mathematician Georg Cantor (1845-1918) developed set theory while researching trigonometric 
series. This presentation explores basic set definitions and operations.
F o u n d a t i o n
Sets form the basis for 
mathematical relationships and 
structures.
A p p l i c a t i o n s
Used in geometry, probability, 
and throughout mathematics.
O r i g i n
Developed by Georg Cantor in 
the 19th century.
Sets and their 
Representations
Sets are well-defined collections of distinct objects. They 
exist in everyday contexts and mathematics.
1
Odd 
Number
s < 10
1, 3, 5, 7, 9
2
English 
Vowels
a, e, i, o, u
3
Prime 
Factors 
of 210
2, 3, 5, 7
4
Rivers of India
Ganga, Yamuna, Brahmaputra, etc.
Page 4


Sets
I n t r o d u c t i o n
Sets are fundamental to modern mathematics, used across virtually all branches. They provide the 
foundation for relations, functions, geometry, sequences, probability, and many other mathematical 
concepts.
German mathematician Georg Cantor (1845-1918) developed set theory while researching trigonometric 
series. This presentation explores basic set definitions and operations.
F o u n d a t i o n
Sets form the basis for 
mathematical relationships and 
structures.
A p p l i c a t i o n s
Used in geometry, probability, 
and throughout mathematics.
O r i g i n
Developed by Georg Cantor in 
the 19th century.
Sets and their 
Representations
Sets are well-defined collections of distinct objects. They 
exist in everyday contexts and mathematics.
1
Odd 
Number
s < 10
1, 3, 5, 7, 9
2
English 
Vowels
a, e, i, o, u
3
Prime 
Factors 
of 210
2, 3, 5, 7
4
Rivers of India
Ganga, Yamuna, Brahmaputra, etc.
Special Sets in Mathematics
Mathematics features several standard sets identified by universal symbols. The most common include 
natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R).
In set notation, capital letters (A, B, C) denote sets, while lowercase letters (a, b, c) represent elements, 
objects, or members of sets.
Natural Numbers 
(N)
Counting numbers: 1, 2, 
3, 4, ...
Integers (Z)
Whole numbers and 
their negatives: ..., -2, 
-1, 0, 1, 2, ...
Rational Numbers 
(Q)
Numbers expressible as 
fractions p/q where p, q 
are integers and qb0
Real Numbers (R)
All rational and 
irrational numbers
Page 5


Sets
I n t r o d u c t i o n
Sets are fundamental to modern mathematics, used across virtually all branches. They provide the 
foundation for relations, functions, geometry, sequences, probability, and many other mathematical 
concepts.
German mathematician Georg Cantor (1845-1918) developed set theory while researching trigonometric 
series. This presentation explores basic set definitions and operations.
F o u n d a t i o n
Sets form the basis for 
mathematical relationships and 
structures.
A p p l i c a t i o n s
Used in geometry, probability, 
and throughout mathematics.
O r i g i n
Developed by Georg Cantor in 
the 19th century.
Sets and their 
Representations
Sets are well-defined collections of distinct objects. They 
exist in everyday contexts and mathematics.
1
Odd 
Number
s < 10
1, 3, 5, 7, 9
2
English 
Vowels
a, e, i, o, u
3
Prime 
Factors 
of 210
2, 3, 5, 7
4
Rivers of India
Ganga, Yamuna, Brahmaputra, etc.
Special Sets in Mathematics
Mathematics features several standard sets identified by universal symbols. The most common include 
natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R).
In set notation, capital letters (A, B, C) denote sets, while lowercase letters (a, b, c) represent elements, 
objects, or members of sets.
Natural Numbers 
(N)
Counting numbers: 1, 2, 
3, 4, ...
Integers (Z)
Whole numbers and 
their negatives: ..., -2, 
-1, 0, 1, 2, ...
Rational Numbers 
(Q)
Numbers expressible as 
fractions p/q where p, q 
are integers and qb0
Real Numbers (R)
All rational and 
irrational numbers
Set Notation
Set notation uses specific symbols to show relationships between elements and sets. We write "a * A" to 
indicate "a belongs to set A" and "b + A" to indicate "b does not belong to set A. "
Examples: In the set V of English vowels, a * V but b + V. In the set P of prime factors of 30, 3 * P but 15 
+ P .
1
Belongs To ( *)
Indicates element 
membership in a set. 
Example: 3 * {1, 2, 3, 4, 5} 
means 3 is in the set.
2
Does Not Belong To 
( +)
Indicates an element is 
not in a set. Example: 6 + 
{1, 2, 3, 4, 5} means 6 is 
not in the set.
3
Methods of 
Representation
Sets can be represented 
in two ways: Roster 
(tabular) form and Set-
builder form.