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.