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2. Index of Presentation
Concept of a Set.
Notation of set.
Notation for set of number’s.
Signs which show the relation between
sets and elements.
Types of sets.
Different between proper sub & sub set.
Different between equal and equivalent
set.

3. Concept of a Set
A set is a well-defined collection
of distinct objects.
Each object is called an element
of the set.

4. Example of Set.
 The collection of all four-legged
dogs is a set.
Each four-legged dog is an element
of the set.
The collection of counting
numbers is a set.
 Each counting number is an element of
the set.

5. Notation of set
o Sets are denoted by capital
letters.
o i.e. A,B,C……..X,Y,Z.
o A={1,2,3}.
o B={a,b,c}.
o C={cat, monkey}.

6. Notation of set
cont……
o And an element denoted by small
letter.
o i.e.
o a,b,c…….x,y,z.
o A={1,2,3}.
o B={a,b,c}.
o C={cat,monky}.

7. Notation for set of number’s.
o Natural numbers.
o Those numbers start from
one(1) to onward like that.
o N={1,2,3……..}.
o Whole numbers.
o Those number start from
zero(0) to onward like that.
o W={0,1,2,3……}.

8. Cont……
• Integers numbers.
• Those numbers written onward &
downward from zero(0) like
that.
• Z={….-3,-2,-1,0,1,2,3……}.
• Even or Odd numbers .
• Those numbers written on even
or Odd.
• i.e.
• E={2,4,6,8…..}. O={1,3,5,7…..}.

9. Cont…..
• Prime numbers.
• Those number divide into own
number.
• i.e.
• P={2,3,5,7,11…..}.
• Expect own no any table divide
these type number.

10. Types of sets.
o Following the types of sets.
Sub set.
Proper sub set.
Super subset.
Equal set.
Equivalent set.
Universal set.
Ordered pair set.

11. Sub set.
• Let A&B are two sets then all
the elements of sets A are
present in set B the set a is
called sub set of B set
• A={2,4,6}
• B={1,2,3,4,5,6,7}
• or
BA
AB BA

12. Cont…..
• Note:
• Null set is sub set of every set
is expressed by {} or.
• Every non empty set has sub
sets as 2n where n is number of
elements every sets sub set
itself.

13. • i.e.
• A={a,b}
• No: of sub sets =2n=22=4.
• i {}.
• ii {a}.
• iii {b}.
• iv {a,b}.
Cont…..

14. Proper sub set
• Let A&B are two sets if A is a
sub set of B and if there exists
at least one element in that is
not in A.
• A={a,d}
• B={a,b,d}
»or
BA
AB BA

15. Different between proper sub &
sub set
• Proper sub set
• It is only sub
set of set
• Sub set
• It is may be
itself or set

16. Super set
• If A is a sub set of B then B is
called a super set of A.

17. Equal and equivalent sets
• Two sets A and B are equal
mines each of element are same
set A’s element belongs to set B
• i.e.
• A={a,b,c}
• B={a,b,c}
• A=B or B=A

18. Equal and equivalent sets
cont….
• Two sets A and B are equivalent
miens number of element same
but object are not same
• i.e.
A={cat,hours,monky}
• B={egg,milk,mango}
BA 

19. Different Between equal and
equivalent set
Equivalent set:
• Number of
element are same.
• Elements are
different.
Equal set:
• Number of
element are same.
• Elements are also
same.

20. Universal set
• It is the set of all elements that
may be admitted as member of
all the other sets considered
during a given discussion of set
• This set denoted by capital U or
X
• i.e.
• A={a,b,c} B={d,e,f}
• C={a,b,c,d,e,f}
• C is a universal set of A and B

21. Finite and infinite sets
• Those set have limited number
of elements or objects
• i.e.
• A={1,2,3,4,5}
• B={one dozen eggs}
• C={7starts}

22. Cont…..
• Those sets have on limited
numbers of elements or objects
• i.e.
• A={start under the sky}
• B={all pens in the world}