An analysis and presentation of a survey conducted on a group of 500 people to analyze the impact of celebrity, jingle and taglines in an advertisement.
Presentation for Business Mathematics Practical Assignment
3. DEFINITION OF SET
Set A well-defined
collection of distinct
objects.
Elements of a Set can be
anything (i.e. numbers,
characters, other sets,
words, etc.)
Set Not a Set
Well
Defined
and Distinct
Not
Well
Defined
Not Distinct
{1, 2, 3, 4} Presidents {1, 1, 2, 2}
3
4. REPRESENTATION OF SETS
Roster Form All
elements are listed,
enclosed within braces,
separated by commas.
Set-Builder Form All
elements of the set
possess a common
property which is not
possessed by elements
outside the set.
Roster
Form
Set – Builder
Form
{1, 2, 3, 4} {x | x ∈ N and x < 5}
{-3, -2, -1, 0,
1, 2, 3}
{y | y ∈ Z and y2 < 10}
4
6. TYPES OF SETS
Finite Set A set having
a finite number of
elements is called a Finite
Set.
Infinite Set A set in
which the number of
elements is not finite is
called Infinite Set.
TYPES OF SETS
FINITE
A = {1, 2, 3}
B = {x | x∈N, x<5}
INFINITE
A = {1, 2, 3, ….}
B = {x | x∈N, x>5}
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7. TYPES OF SETS
Singleton Set A set
having only one element
is called a Singleton Set.
Empty Set A set
having no element is
called an empty set or a
null set. It is denoted by
∅ or { }.
TYPES OF SETS
SINGLETON
A = {1}
B = {b}
EMPTY
A = { }
B = ∅
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9. RELATIONSHIP BETWEEN SETS
Equal Sets If two sets
have the exact same
elements, they are called
equal sets. It is denoted
by A = B.
Equivalent Sets If two
sets have the same
number of elements,
they are called equivalent
sets. It is denoted by A ≅
B.
RELATIONSHIP
BETWEEN SETS
EQUAL
A = {1, 2, 3}
B = {1, 2, 3}
EQUIVALENT
A = {1, 2, 3}
B = {1, 4, 9}
9
11. SUBSET OF A SET
Subset of a Set If all
elements of Set A belong
to Set B then Set A is a
subset of Set B. It is
denoted by A ⊆ B.
Proper Subset If all
elements of Set A are
elements of Set B and A ≠
B then Set A is a proper
subset of Set B. It is
denoted by A ⊂ B.
SUBSET
PROPER
SUBSET
A = {1, 2, 3}
B = {1, 2, 3, 4, 5}
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12. SUBSET OF A SET
Every Set is a subset of
itself.
Empty Set is a subset of
all sets.
Equal Sets are subsets of
each other.
A = {1, 2, 3} & B = {1, 2, 3}
SUBSETS OF A
{1, 2, 3}
∅
B
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13. POWER SET
Power Set The set that
contains all subsets of Set
A is called the Power Set
of Set A. It is denoted by
P(A).
A = {1, 2, 3}
P(A)
∅
{1}
{2}
{3}
{1, 2}
{1, 3}
{2, 3}
{1, 2, 3}
13
14. IF SET A HAS n ELEMENTS
P(A) has 2n elements.
Set A has 2n subsets.
Set A has 2n-2 proper
subsets
A = {1, 2, 3}
n = 3 2n = 8 POWER SET
SUBSETS
∅
PROPERSUBSETS
{1}
{2}
{3}
{1, 2}
{1, 3}
{2, 3}
{1, 2, 3} 14
16. UNIVERSAL SET
Universal Set A parent
set of which all different
sets are subsets of is
called the Universal Set
during that situation.
U = {1, 2, 3, 4}
1 2 3
4
U
A B
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18. VENN DIAGRAM
Venn Diagram A Venn
Diagram is a diagram in
which sets are
represented pictorially by
circles enclosed in a
rectangle while common
elements are represented
by intersection of circles.
A = {1, 2}
B = {2, 3}
1 2 3
4
U
BA
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19. OPERATIONS ON SET
Union of Sets
Intersection of Sets
Complement of a Set
Difference of Sets
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20. UNION OF SETS
The Union of Sets A and
B is the set of all
elements that belong to
either A or B.
U = {1, 2, 3, 4}
A = {1, 2}
B = {2, 3}
A ∪ B = {1, 2, 3}
1 2 3
4
U
A B
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21. INTERSECTION OF SETS
The Intersection of Sets
A and B is the set of all
elements that belong to
both A and B.
U = {1, 2, 3, 4}
A = {1, 2}
B = {2, 3}
A ∩ B = {2}
1 2 3
4
U
A B
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22. COMPLEMENT OF A SET
The Complement of Set
A is the set of all
elements that belong to
U and do not belong to
A.
U = {1, 2, 3, 4}
A = {1, 2}
A’ = U – A = {3, 4}
1 2 3
4
U
A B
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23. DIFFERENCE OF TWO SETS
The Difference of Sets A
and B is the set of all
elements that belong to
A and do not belong to B.
U = {1, 2, 3, 4}
A = {1, 2}
B = {2, 3}
A - B = {1}
1 2 3
4
U
A B
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27. JINGLES AND MUSIC EFFECTS
Advantages
Easy to Remember
Differentiates the Product
Creates Bond between Brand and
Customer
Disadvantages
Lack of Universal Appeal
Distracts from the Verbal Message
Customer Attitude may deteriorate
due to Repetition
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28. TAGLINES AND SLOGANS
Advantages
Builds a Brand Identity
Cannot be used by Competitors
Can be used in promotions other
than Advertising
Disadvantages
Lack of Universal Appeal
Often missed or forgotten
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30. SURVEY QUESTION
Which aspect(s) of the advertisement – ‘Navratna Oil – Raahat Raja’
make(s) it the most memorable for you?
a) Celebrity – Amitabh Bachchan
b) Jingle – Navratna Aazmaye
c) Tagline – Thanda Thanda Cool Cool
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36. Analysis
OPTION SYMBOLIC VALUE
A n(A) 265
B n(B) 250
C n(C) 226
A and B n(A ∩ B) 89
A and C n(A ∩ C) 73
B and C n(B ∩ C) 84
All A, B and C n(A ∩ B ∩ C) 29
At Least One n(A ∪ B ∪ C) 524
None n((A ∪ B ∪ C)’) 26
36
132
29
98
106
A B
44 55
60
26C
U
37. Analysis
OPTION SYMBOLIC VALUE
Only A n(A ∩ B’ ∩ C’) 132
Only B n(A’ ∩ B ∩ C’) 106
Only C n(A’ ∩ B’ ∩ C) 98
Only A and B n(A ∩ B ∩ C’) 60
Only A and C n(A ∩ B’ ∩ C) 44
Only B and C n(A’ ∩ B ∩ C) 55
Not A n(A’) 285
Not B n(B’) 300
Not C n(C’) 324
37
132
29
98
106
A B
44 55
60
26C
U
39. Conclusions
If only one of them can be
employed, then the priority should
be as follows: -
TaglineJingleCelebrity
39
132
29
98
106
A B
44 55
60
26C
U
40. Conclusions
If a combination of any two is
employed, the priority for maximum
target audience should be: -
Jingle +
Tagline
Celebrity
+ Tagline
Celebrity
+ Jingle
40
132
29
98
106
A B
44 55
60
26C
U
41. Conclusions
If a combination of any two is
employed, the priority for maximum
cost effectiveness should be: -
Celebrity
+ Jingle
Jingle +
Tagline
Celebrity
+ Tagline
41
132
29
98
106
A B
44 55
60
26C
U
42. Conclusions
When all three of them are
employed, the impact is: -
TaglineJingleCelebrity
42
132
29
98
106
A B
44
60
26C
U
55