Set theory definitions are listed in this ppt.

1. WELCOME
PRESENTED
BY
S.P.ABINAYA

2. STANDARD 9
TERM1
VOLUME 2

3. THEORY OF SETS
 The basic ideas of set theory were developed by
the GERMAN MATHEMATICIAN
GEORG CANTOR ( 1845 – 1918 )
 The concept of set is vital to mathematical thought
and is being used in almost every branch of
mathematics.
 Understanding set theory helps us to see things in
terms of systems, to organize things into sets and
begin to understand logic.

4. SET
 A set is a collection of well defined objects. The
objects of a set are called elements or members of
the set.
 Example – 1 The collection of male students in
your class
 Example – 2 The collection of numbers 2,4,6,10
and 12.
 € refers “ is an element of ” or “ belongs to ”

5. CARDINAL NUMBER
 The number of elements in a set is called the
cardinal number of the set.
 The cardinal number of a set A is denoted by n(A)
 Example : Consider the set A = {1,2,3,4,5} the
cardinal number of A is 5 i.e., n(A)=5

6. THE EMPTY SET
 A set containing no elements called the empty set
or Null set or Void set.
 The empty set is denoted by the symbol
Φ or { }

7. FINITE AND INFINITE SETS
 If the number of element in the set is zero or finite,
then the set is called finite set. The cardinal
number of a finite set is finite.
 A set is set to be an infinite set if the number of
element in the set is not finite. The set of whole
numbers is an infinite set .
 A set containing only one element is called a
singleton set.

8. SUBSET and PROPER SUBSET
 A set X is a subset of set Y if every element of X is
also an element of Y. In symbol , X C Y.
 A set X is said to be a proper subset of set Y if
X C Y and X ≠ Y. In symbol, X C Y. Y is called
super set of X.

9. PROPER SET
 The set of all subsets of A is aid to be the power
set of the set A.
 The power set of a set A is denoted by P(A).

10. THANK YOU
HAVE A NICE DAY