Page 1
SET THEORY
? Set: A collection of well defined objects.
? Sets are usually denoted by capital letters A, B, C
etc. and their elements are denoted by a, b, c etc.
? Few examples:
? The collection of vowels in English alphabets. This
set contains five elements i.e. a,e,i,o,u.
? The set of 3 cycle companies of India. This set
contains 3 elements i.e. Hero, Avon, Suncross.
? The set of 4 rivers in India. This set contains 4
elements i.e. Ganga, Yamuna, Beas, Narmada,
Kaveri.
? The collection of good cricket players of India is
not a set
Page 2
SET THEORY
? Set: A collection of well defined objects.
? Sets are usually denoted by capital letters A, B, C
etc. and their elements are denoted by a, b, c etc.
? Few examples:
? The collection of vowels in English alphabets. This
set contains five elements i.e. a,e,i,o,u.
? The set of 3 cycle companies of India. This set
contains 3 elements i.e. Hero, Avon, Suncross.
? The set of 4 rivers in India. This set contains 4
elements i.e. Ganga, Yamuna, Beas, Narmada,
Kaveri.
? The collection of good cricket players of India is
not a set
REPRESENTATION OF A SET
Roster
Form
Set Buider
Form
Page 3
SET THEORY
? Set: A collection of well defined objects.
? Sets are usually denoted by capital letters A, B, C
etc. and their elements are denoted by a, b, c etc.
? Few examples:
? The collection of vowels in English alphabets. This
set contains five elements i.e. a,e,i,o,u.
? The set of 3 cycle companies of India. This set
contains 3 elements i.e. Hero, Avon, Suncross.
? The set of 4 rivers in India. This set contains 4
elements i.e. Ganga, Yamuna, Beas, Narmada,
Kaveri.
? The collection of good cricket players of India is
not a set
REPRESENTATION OF A SET
Roster
Form
Set Buider
Form
ROSTER FORM
? This method is also called Tabular Method.
? In this, a set is described by listing elements,
separated by commas, within braces { }
? The collection of vowels in English alphabets. This
set contains five elements i.e. {a,e,i,o,u }
? If A is the set of even natural numbers, then
A = {2, 4, 6, …….. }
? If A is the set of all prime numbers less than 11, then
A = {2, 3, 5, 7}
? Note:
? The order of writing the elements of a set is
immaterial.
? An element of a set is not written more than once.
Page 4
SET THEORY
? Set: A collection of well defined objects.
? Sets are usually denoted by capital letters A, B, C
etc. and their elements are denoted by a, b, c etc.
? Few examples:
? The collection of vowels in English alphabets. This
set contains five elements i.e. a,e,i,o,u.
? The set of 3 cycle companies of India. This set
contains 3 elements i.e. Hero, Avon, Suncross.
? The set of 4 rivers in India. This set contains 4
elements i.e. Ganga, Yamuna, Beas, Narmada,
Kaveri.
? The collection of good cricket players of India is
not a set
REPRESENTATION OF A SET
Roster
Form
Set Buider
Form
ROSTER FORM
? This method is also called Tabular Method.
? In this, a set is described by listing elements,
separated by commas, within braces { }
? The collection of vowels in English alphabets. This
set contains five elements i.e. {a,e,i,o,u }
? If A is the set of even natural numbers, then
A = {2, 4, 6, …….. }
? If A is the set of all prime numbers less than 11, then
A = {2, 3, 5, 7}
? Note:
? The order of writing the elements of a set is
immaterial.
? An element of a set is not written more than once.
SET BUILDER FORM
? This form is also called Property Form.
? In this, a set is represented by stating all the
properties P(x) which are satisfied by the
elements x of the set and not by other element
outside the set.
? If A is the set of even natural numbers, then
A = {x: x ? N, x = 2n, n ? N}
A = {x: x is a natural number and x = 2n for n ? N}
? If A = {0, 1, 4, 9, ……}
A = {x
2
: x ? N}
? If B = The set of all real numbers greater than -3 and
less than 3
B = {-3<x<3 : x ? R}
Page 5
SET THEORY
? Set: A collection of well defined objects.
? Sets are usually denoted by capital letters A, B, C
etc. and their elements are denoted by a, b, c etc.
? Few examples:
? The collection of vowels in English alphabets. This
set contains five elements i.e. a,e,i,o,u.
? The set of 3 cycle companies of India. This set
contains 3 elements i.e. Hero, Avon, Suncross.
? The set of 4 rivers in India. This set contains 4
elements i.e. Ganga, Yamuna, Beas, Narmada,
Kaveri.
? The collection of good cricket players of India is
not a set
REPRESENTATION OF A SET
Roster
Form
Set Buider
Form
ROSTER FORM
? This method is also called Tabular Method.
? In this, a set is described by listing elements,
separated by commas, within braces { }
? The collection of vowels in English alphabets. This
set contains five elements i.e. {a,e,i,o,u }
? If A is the set of even natural numbers, then
A = {2, 4, 6, …….. }
? If A is the set of all prime numbers less than 11, then
A = {2, 3, 5, 7}
? Note:
? The order of writing the elements of a set is
immaterial.
? An element of a set is not written more than once.
SET BUILDER FORM
? This form is also called Property Form.
? In this, a set is represented by stating all the
properties P(x) which are satisfied by the
elements x of the set and not by other element
outside the set.
? If A is the set of even natural numbers, then
A = {x: x ? N, x = 2n, n ? N}
A = {x: x is a natural number and x = 2n for n ? N}
? If A = {0, 1, 4, 9, ……}
A = {x
2
: x ? N}
? If B = The set of all real numbers greater than -3 and
less than 3
B = {-3<x<3 : x ? R}
TYPES OF SETS
? Empty Set: A set is said to be empty or null or void
set if it has no element and it is denoted by f.
? In Roster Method, it is denoted by { }
? Examples:
? A = {x: x ? N, 7 < x < 8} = f
? B = {x ? R : x
2
= -2} = f
?C = Any Indian company which is into Automobiles,
Clothing, Plastics, Paper, Processed Food
? Note:
? {f} is not a null set, since it contains f as an element.
? {0} is not a null set, since it contains 0 as an element.
E
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