set{m adeel rajput}
TRANSCRIPT
Topic: Set.Present by:
Muhammad Adeel RajputBS(IT) 1st semester
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.
Concept of a Set
A set is a well-defined collection of distinct objects.
Each object is called an element of the set.
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.
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}.
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}.
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……}.
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…..}.
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.
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.
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
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.
• i.e.• A={a,b}• No: of sub sets =2n=22=4.• i {} .• ii {a}.• iii {b}.• iv {a,b}.
Cont…..
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
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
Super set
• If A is a sub set of B then B is called a super set of A.
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=Bor B=A
Equal and equivalent setscont….
• 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
Different Between equal and equivalent setEquivalent
set:
• Number of element are same.
• Elements are different.
Equal set:• Number of
element are same.
• Elements are also same.
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
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}
Cont…..
• Those sets have on limited numbers of elements or objects
• i.e.• A={start under the sky}• B={all pens in the world}
Thanks for your attentio
n.