CONCEPTS OF SETS AND USE OF VENN DIAGRAM OVERVIEW

1. Presentation topic
Sets using venn diagrams
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

2. Objectives of presentation(cont’d)
Concept of set with examples
Set notation
Methods how to describe a set
Types of set
Cardinality of set and power set
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

3. Objectives of presentation
 Venn diagrams
 representing disjoint sets using
venn diagrams
 Representing sub sets using venn
diagrams
 Concept of union of two sets
 Concept of intersection of two sets
 Concept of complement of a set
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

4. Set
• Any collection
• Of any thing(objects/elements/members)
• Unordered
• Well defined
• {@,#,$,%}
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

5. Examples of set(cont’d)
N={0,1,2,3,………}
N is a set of natural number.
Z={………,-2,-1,0,1,2,……….}
Z is set of integers
Integers are of two types
1. Positive
{1,2,3,4,…….}
2. Negative
{….-4,-3,-2,-1}
Note: repetition of element is not allowed in sets. 5
By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

6. Examples of set
Set of
1.Non positive integers
2.Non negative integers
NP={….,-2,-1,0}
NN={0,1,2,…...}
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

7. Set notation
 The act ,process, method or instance of
representing…..
Elements/members/objects of a sets
 Upper case letters to represent sets
Lower case letters to represent elements
 Symbol  means “it belongs to ” “it does
not belongs to”
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

8. Describing a set
• A set can be described in two ways.
1. listing all elements of set
A={0,1,2,3,4,5,6,7,8,9}
2. writing description of elements of the set
A={set of whole numbers less then ten}
Note: concerning set all elements must be inside
pair of curly braces.
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

9. Types of set
a. Universal set
b. Empty set
c. Equal set
d. Finite set
e. Infinite set
f. Sub set
g. Super subset
h. Power set
i. Disjoint set
j. Multi set
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

10. Cardinality of set and power set
• Means number of elements in that set
• S
S={1,2,3}
so cardinality of set “S” is
S=3
• Power set means
set of all subsets of set “S”
• Cardinality of p(s)= 2n
p(s)={{},{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3}}
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

11. Venn diagram
Diagrams make mathematics easier
because they help us to see the whole
situation at a glance. The English
mathematician John Venn
(1834–1923) began using diagrams to
represent sets. His diagrams are now
called Venn diagrams.
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

12. Venn diagram(cont’d)
• Sets are represented in a Venn diagram by
circles drawn inside a rectangle representing
the universal set.
U
A
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

13. Complement of a set
The region outside the circle represents the
complement of the set.
U
A
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

14. Intersection of sets
The overlapping region of two circles
represents the intersection of the two sets.
U
A B
intersection
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

15. Union of sets
• Two circles together represent the union of the
two sets. Two circles together represent the
union of the two sets.
BA
U
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

16. Disjoint sets
• When two sets are disjoint, we can draw the
two circles without any overlap.
A B
U
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK

17. Subset
• When one set is a subset of another, we can
draw its circle inside the circle of the other set.
B
A
UB is a subset
Of A
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By SAJID BS(BI) Student at Khushal Khan
Khattak University of KARAK