Online test for class 8 - EM - Algebraic Expressions - Part-2

 Online test Prepared by Basa Raja Gopal SA(Maths) ZPHS Kathalapur Jagtial dist

Online test for class 8 - EM - Algebraic Expressions- Part-1

 Online test Prepared by Basa Raja Gopal SA(Maths) ZPHS Kathalapur Jagtial dist

Online Test for Level-3 -Telugu Medium - బీజీయ సమాసాలు Part-2

Online test Prepared by Basa Raja Gopal SA(Maths) ZPHS Kathalapur Jagtial dist

Online Test for Level-3 - Telugu Medium - బీజీయ సమాసాలు

Online test Prepared by Basa Raja Gopal SA(Maths) ZPHS Kathalapur Jagtial dist

Online worksheet for class 9 EM - LE's in 2 Variables

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Online worksheet for class 7 TM - త్రిభుజాల నిర్మాణం

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Online worksheet for class 10TM - వృత్త ఖండ వైశాల్యం

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Online worksheet for class 10 EM - Similar triangles

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Online worksheet for class 7th Em-triangles

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Maths online worksheet for class 7th EM - Data Handling-2

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Maths online worksheet for class 7EM -Data Handling

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Maths online worksheet for class 10EM- Polynomials - 1

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial district

Maths online worksheet for class 7EM - integers-1

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial dstrict

Maths work sheet for class 10EM- statistics-Ogive curves-2

 This Online worksheet Prepared by

Soma Chandra Prakash

SA(Maths) @ ZPHS Satharam, Jagtial dstrict

Maths online worksheet for class 10EM- Ogive curves

 This Online worksheet Prepared by

Vadlakonda Srikanth

SA(Maths) @ ZPHS Dharoor

TMF President Jagtial dstrict

Maths online worksheet for class 9 TM-గోళం - ఉపరితల వైశాల్యం

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

TMF President Jagtial dstrict

Maths online worksheet for class 9 TM - ఉపరితల వైశాల్యం మరియు ఘన పరిమాణం

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

TMF President Jagtial dstrict

Maths Online worksheet for class 8 TM - ఘాతాంక న్యాయాలు

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

TMF President Jagtial dstrict

Maths online worksheet for class 7EM- Ratio and its Applications

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

TMF President Jagtial dstrict

Maths online worksheet for class 9 EM- statistics- introduction

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Maths online worksheet 10 EM - Median and Mode

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Maths worksheet for class 7 EM - Triangle and Its properties-2

Prepared by BASA RAJA GOPAL SA(Maths) ZPHS Kathalapur

Give your feedback in comment box

Online quiz for Class 10 EM - Complete Sets Chapter

 Prepared by BASA RAJA GOPAL SA(Maths) ZPHS Kathalapur

Give your feedback in comment box

Maths worksheet for class 10 EM - Basic operations on sets - 2

This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Maths worksheet for class 8 EM - Compound Ratio, Profit and Losses - 2

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Maths worksheet for class 8 EM - Compound Ratio, Profit and Losses

  Prepared by BASA RAJA GOPAL SA(Maths) ZPHS Kathalapur

Give your feedback in comment box

Online worksheet for class 10 EM - Statistics - Mean

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Online worksheet for class 9 TM - స్థూపము - ఉపరితల వైశాల్యం - 1

 Prepared by BASA RAJA GOPAL SA(Maths) ZPHS Kathalapur

Online worksheet for class 9th EM - The elements of geometry-1

Online worksheet for class 9 EM - The elements of geometry-2

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Online worksheet for class 8 telugu medium - ఘన మూలాలు

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Online worksheet for class 7th EM on triangle and it's properties

 

Online worksheet for class 7 English medium triangle and its properties

 This Online worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district 

Online worksheet for class 7 On Lines and Angles

This Onlline worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district 

Online worksheet for class 8 English medium Powers and Exponents

This Onlline worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district 

Online worksheet for class 7 English medium Simple equations-1

This Onlline worksheet Prepared by

Vadlakonda Srikanth

 SA(Maths) @ ZPHS Dharoor

 TMF President Jagtial district

Online worksheet for class 7 English Medium On Simple equations-2

Prepared by Siripuram Mahesh SA(Maths) ZPHS Bhupathipur

Siripuram Mahesh

 SA(Maths) @ZPHS Bhupathi Pur

Jagtial District

Online worksheet for class 9th EM - Remainder theorem from Polynomials

This Online worksheet is Prepared by Basa Raja Gopal SA(Maths)@ZPHS Kathalpaur, Jagtial District.

Give your valuable feedback in Comment Box

Sets-4th-class 10- Operations on Sets- Union of two sets - English medium-with examples and model problems

In this page,

we are going to know the "Operations on sets"

There are Three Basic operations. Those are Union of sets, intersection of sets and difference of sets.

Before going to know the operations on sets

first we know the Introduction of sets and Types of sets

Now let us learn about,

 

Union of two sets:

Let A and B are two Non-empty sets

"A set with elements from set A and Set B is called Union set of set A and set B"

we denote Union set of A and set B as "A∪B".

we read as "A union B"

The element of A∪B is an element of either set A or set B or Both.

A∪B is represents in Set builder form as follows

A∪B={x : x 𝞊 A or x 𝞊 B }

Example-1.

A={1, 2, 3, 4 } and B={2, 4, 6, 8, 9 }

All the elements from two sets, write in one set

(keep in mind, No element can repeat in a set)

∴ A∪B={1, 2, 3, 4, 6, 8, 9 }

Example-2.

P={a, e, i, o, u } and Q={a, b, c, d, e }

All the elements from two sets, write in one set

∴ P∪Q={a, e, i, o, u, b, c, d }

(write all elements from first set then write elements from second set. If any element member in two sets , write only one time)

Example-3.

A={2, 3, 5, 7 } and Ø ={ }

All the elements from two sets, write in one set

 A∪Ø={2, 3, 5, 7 }

∴ A∪Ø=A

(write all elements from first set then write elements from second set. But here no element in second set because it is Null set. So we get first set as answer )

Example-4.

A={4, 6, 8, 9, 10 } and A={4, 6, 8, 9, 10 }

write all elements from first set then write elements from second set.

 A∪A={4, 6, 8, 9, 10 }

∴ A∪A=A

(All the elements in two sets are same and no element repeats. So we got answer as first set)

Note:

1. AUB = BUA 

2. AUØ = ØUA = A

3. AUA = A 

4. AUB is super set to set A and set B

5. set A is subset to AUB. (A ⊂ AUB)

6. set B is subset to AUB. (B ⊂ AUB)

7. If A ⊂ B, then AUB = BUA = B 

7. If B ⊂ A, then AUB = BUA = A

Online worksheet for class 8 వర్గ సంఖ్యలు మరియు వాటి ధర్మాలు

worksheet for class 9 Algebraic identities Both Media

This Online Worksheet Prepared by V. Venkata Swamy SA(Maths) ZPHS kathalapur

V. Venkata Swamy

 SA(Maths) @ZPHS KathalaPur

Jagtial District

worksheet for class 9english medium Algebraic Identities

Prepared by Vadlakonda Srikanth SA(Maths) ZPHS Dharoor TMF President Jagtial district

Work sheet for class 8 english medium LE in one variable

Prepared by Vadlakonda Srikanth SA(Maths) ZPHS Dharoor TMF President Jagtial district

Online worksheet for class 10 english medium Basic operations on sets

Prepared by Siripuram Mahesh SA(Maths) ZPHS Bhupathipur

Siripuram Mahesh

 SA(Maths) @ZPHS Bhupathi Pur

Jagtial District

online worksheet for class 8 telugu medium పౌన పున్య పట్టికలు, రేఖా చిత్రాలు

Prepared by Vadlakonda Srikanth SA(Maths) ZPHS Dharoor

Vadlakonda Srikanth

 SA(Maths)

President, TMF Jagtial

worksheet for class 10 Telugu medium త్రికోణమితీయ నిష్పత్తులు

 This online work sheet  Prepared by V.Venkata Swamy

V. Venkata Swamy SA(Maths)

ZPHS KATHALAPUR

JAGTIAL DISTRICT

worksheet for class 7 on area of triangle for telugu medium

Prepared by Vadlakonda Srikanth SA(Maths) ZPHS Dharoor Jagtial District President TMF Jagtial District

worksheet for class 9 English medium on rationalization of real numbers

Prepared by V.Venkata Swamy SA(Maths) ZPHS Kathalapur Jagtial District

worksheet for class 10 telugu medium ప్రాథమిక అనుపాత సిద్ధాంతం

Prepared by D.Sandhya Rani CRT(Maths) KGBV Kathalapur Jagtial District

Worksheets for class 10 on sets for telugu medium

Prepared by D.Sandhya Rani CRT(Maths) KGBV Kathalapur Jagtial District

Worksheet on zeroes of a polynomial for telugu medium

Prepared by D.Sandhya Rani CRT(Maths) KGBV Kathalapur Jagtial District

Worksheet for class 7 multiplication and division of fractions

Prepared by D.Sandhya Rani CRT(Maths) KGBV Kathalapur Jagtial District

Online worksheet for class 9 telugu medium త్రిభుజాల సర్వ సమానత్వం

Prepared by D.Sandhya Rani CRT(Maths) KGBV Kathalapur Jagtial District

Online test for class 9 - Operations on Real numbers

Prepared by V.Venkata Swamy SA(Maths) ZPHS Kathalapur Jagtial District

Worksheet for class 10 english medium on sets

 Prepared by V. Venkata Swamy, SA(Maths), ZPHS Kathalapur, Jagtial district

Worksheet for class 8 English medium on Decimal representation

worksheet for class 10 English medium on similar triangles-1

 

worksheet for class 10 telugu medium on సరూప త్రిభుజాలు - 2

 

Worksheet for class 8 English medium on Linear equations in one variable

Prepared by V. Venkata Swamy, SA(Maths), ZPHS Kathalapur, Jagtial Dist

Worksheet for class 10 English medium on Logarithms-2 from Real numbers

Prepared by V. Venkata Swamy, SA(Maths), ZPHS Kathalapur, Jagtial Dist.

Worksheet for class 10 English medium on SETS-1

Prepared by V. Venkata Swamy, SA(Maths), ZPHS Kathalapur, Jagtial Dist

Worksheet for class 10 Telugu medium on సరూప త్రిభుజాలు - 1

కృత్య పత్రము - సరూప త్రిభుజాలు

Prepared by V. Venkata Swamy, SA (Maths), ZPHS Kathalapur, Jagtial district

Worksheet for class 10 on Logarithms -1 from Real numbers

worksheet for class 9 Telugu medium on Lines and Transversal

సరళ రేఖలు - తిర్యగ్రేఖ -  9వ తరగతి

కృత్య పత్రం (worksheet)

worksheet on Real numbers for class 9 English medium

This worksheet for class-9 English medium students (based on SCERT Module)

15 questions from Real numbers

Students!

Do the solutions in your notebook, show it to your teacher whenever required. 

See your score instant by clicking "view score"

Screen shot your score page and send to your teacher

sets-3rd-class 10-mathematics-English medium-subset-proper subset-super set-universal set-equal sets

 Sets-class.10-mathematics

Click the link about "Definition of sets-Roster form-Set builder form"

Click the link about "Types of sets-Null set-Infinite set-Equal sets"

1.Subset & Super set:

Let A and B are two Non-empty sets.
If Every element of set A is a member of Set B, then set A is called subset of Set B.

we write as A⊆B
read as "A is subset of B"

And set B is called Super set of set A

we denotes B⊃A
read as "B is super set of A"

NOTE:

Sets A and B are EQUAL SETS,
If and only if every element of set A is a member of set B
and every element of set B  is a member of set A.

"If A⊆B and B⊆A then A and B are called Equal sets"

"If A=B then A⊆B and B⊆A"

NOTE:

Null set(∅) is subset to every set

And

Every set is subset to itself

Suppose A={3, 4, 5, 7 } and ∅={   }

∅ has no elements
So,  ∅ is subset to A

And every element of set A is member of set A
So, A is subset to A(itself)

Example.1:

A={1, 2, 3, 4} and B={2, 4}

Every element of set B is the element of set A
So
set B is subset of set A
∴ B⊂A

And
set A is called Super set of set B
∴ A⊃B

Example.2:

P is the set of factors of 5
Q is the set of factors of 25

first we know the elements of sets
P={1, 5}
Q={1, 5, 25}

Here Every element of set P is the element of set Q
So
set P is subset of set Q
∴ P⊂Q
And

set Q is called Super set of set P
∴ Q⊃P

Example.3:

X={x/x is a letter of the word "WOLF"}
Y={x/x is a letter of the word "FOLLOW"}

first we know the elements of sets
X={ w, o, l, f }
Y={f, o, l, w}

Here Every element of set X is the element of set Y
So
set X is subset of set Y
∴ X⊂Y

And
Every element of set Y is the element of set X
So
∴ Y⊂X

Here X⊂Y and Y⊂X
So, X, Y are equal sets
∴ X=Y

2.Proper subset:

If every element of set A is a member of set B and atleast one element of set B is not a member of set A then "set A is proper subset of set B"

In other words
If every element of set A is presents in set B but set A is not equal set to set B then set A is called proper subset of set B.

Let A⊂B and A≠B, 
∴ A is proper subset of B

3.Universal set:

A set super set of all sets of under our consideration is called "Universal set"

It is denoted by "U" or "μ"

Here all the sets under our consideration are the subsets to Universal set

For example,

We take all classes in our school as sets

Then

School set is Universal set

Because all class sets are subsets to School set

-------------------------------------------

similarly

In a village,

Let's take male people are one set and 

female people are other set

 Then the set of village people is universal set

--------------------------------------------- 

similarly, 

Prime Numbers and Composite Numbers are belongs to Natural numbers

And,

Natural number set is a super set for Prime Number set and Composite Numbers set 

So,

Set of Natural numbers is Universal set

--------------------------------------------------

worksheet on Real numbers for Telugu medium students

 వాస్తవ సంఖ్యలు  -  కృత్య పత్రం

మొత్తం పాఠం పై 10 Easy ప్రశ్నలు

Worksheet on Real numbers for class 10-whole chapter-Easy concepts

Worksheet on Real numbers for class 10

10 questions from total chapter

Basic(Easy) concepts 

Worksheet- 4 on sets for English medium (definition of sets-roster form-set builder form)

 This worksheet for class-10 English medium students (based on SCERT Module)

20 questions from Sets(definition of sets, roster form and set builder form)

Students!

Do the solutions in your notebook, show it to your teacher whenever required. 

For more about Sets just click definition of sets, roster form and set builder form

worksheet on rational numbers for class 8 english medium

This worksheet for class-8 English medium(based on SCERT Module)

20 questions from Rational numbers

Students!

Do the solutions in your notebook, show it to your teacher whenever required. 

Simply click your answers 

See your score instant by clicking "view score"

Screen shot your score page and send to your teacher

worksheet-3 for class 10 on Fundamental theorem of arithmetic- finding LCM and HCF

 This worksheet for class 10 English medium students

20 questions on "Fundamental theorem of arithmetic" from Real numbers

Students!

See your score instant by clicking "view score"

Screen shot your score page and send to your teacher

worksheet for class 10 -Telugu medium-బహుపదుల విలువలు మరియు శూన్యాలు

 

worksheet-2-telugu medium-finding hcf by Euclid's division algorithm

work sheet-2-for class-10- English medium-find HCF-by Euclid's division algorithm from Real numbers

 

Worksheet-1 for class 10- Euclid's division algorithm from Real numbers

 

Sets-2nd part-10th class-mathematics-English medium-types of sets-null set- singleton set-infinite set-equivalent sets-equal sets

10th class-mathematics-Sets

Types of Sets

1. Null Set or Empty Set

A Set Without elements is called Null Set

Null Set is denoted by  {  } 

The symbol "Ø"  is used to represent a null set

This is read as "pi" 

Cardinal number of Null Set is "ZERO"

i.e.   n(Ø) = 0

Example.1:

A is the set of months of a year having  35 days

No months in a year with 35 days

So A is a Null set

∴ A = {  }    

and cardinal number of A is "zero"

∴ n(A) = 0

Example.2:

C is the set of composite numbers less than 4

Composite numbers are start from 4

That means 4 is the smallest composite number

So there is no composite numbers less than 4

Therefore C is a null set

∴ C = {  }

and

 n(C) = 0

Note:

 Ø, { 0 } ,  { Ø }  are  three different sets

 Ø is a null set

{ 0 } is a set with element "0"

{ Ø } is set with element "Ø"

---------------------------------------------

2. Singleton Set

If A Set contained only One element, It is called Singleton Set

Example.3:

P is the set of even prime numbers

Here even prime number is only 2

So, P = { 2 } 

And     n(P) = 1

Here P is called "Singleton Set"

Example.4:

X is the set of Integers neither negative nor positive

In integers only "0" is not negative and not positive

So, X = { 0 }

And     n(X) = 1

Here X is called "Singleton Set"

Note:

Cardinal number of a Singleton Set is ONE.

---------------------------------------------

3. Finite Set

If a Set contained finite number of elements, it is called Finite Set.

In a Finite set elements are countable(limited).

That means we can count the elements in the set

Note:
Cardinal number of a Finite Set is Whole number.

Example.5:

D is the set of days in a week

∴ D = { Sun, Mon, Tue, Wed, Thu, Fri, Sat }

Elements in the set D are Countable

And     n(D) = 7

So, D is a finite set

Example.6:

F is the set of factors of 24

∴ F = { 1, 2, 3, 4, 6, 8, 12, 24 }

Elements in the set F are Countable

And     n(F) = 8

So, F is a finite set

---------------------------------------------

4. Infinite Set

If a Set contained infinite number of elements, It is called Infinite Set.

Infinite set has unlimited elements.

That means we can not count the elements in the set

A set which is not finite set is called an Infinite set

Note:
Cardinal number of an Infinite Set is not defined.

Examples.7:

S is the set of stars in the Sky

we can't count the stars in the sky
they are unlimited
So, set "S" is an Infinite set

Examples.8:

P is the set of points on a line

we can't count the points on the line
those are unlimited
So, set "P" is an Infinite set

Examples.9:

K is the set of integers less than 5

∴ K = { 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6,............... }

Elements in the set are unlimited
So, set "K" is an Infinite set

Examples.10:

M is the set of multiples of 3

∴ M = { 3, 6, 9, 12, 15, 18,................. }

Elements in the set are unlimited
So, set "M" is an Infinite set

---------------------------------------------

5.Equivalent Sets

Two sets are equivalent, if their number of elements(cardinal number) are same

Elements in equivalent sets could be same or different,

But cardinal number of sets should be same

Example.12:

 A={ 2, 3, 6, 8 } and B={ 1, 2, 3, 4 }

Here  n(A)= 4  and  n(B)=4
Elements are different in both sets
But cardinal numbers are equal

∴ A , B  are Equivalent sets

Example.13:

M={ a, b, c, d, e, f } and N={ 2, 3, 6, 9, 10, 15 }

Here  n(M)= 6  and  n(N)=6

Elements are different in both sets
But cardinal numbers are equal

So,  M and N are Equivalent sets

Example.14:

X={ 0, 3, 6, 9 } and Y={  3, 6, 9 }

Here  n(X)= 4  and  n(Y)=3

Elements are different in both sets
And cardinal numbers are unequal

So,  X and Y are not Equivalent sets

--------------------------------------------------

6.Equal Sets

Two sets are said to be equal sets, if their elements exactly equal

Here elements in both the sets are equal

And cardinal numbers are also equal

If sets A and B are equal sets,

we write them as

 A=B

Example.15:

A={ 1, 7, 2, 9 }   and   B={ 1, 2, 7, 9 }

Elements are equal in above two sets

And n(A)=4 and n(B)=4

So, A and B are equal sets

   

 ∴A=B

Example.16:

C={ a, b, c, d, e }   and  D ={ c, b, e,  d, a }

Elements are equal in above two sets

And n(C)=5 and n(D)=5

∴ C and D are equal sets 

∴ C=D

Example.17:

 E={ a, 2, c, 4 }    and   F={ 1, b, 3, d } 

n(E)=4 and n(F)=4

But Elements are not same in above sets

So,

E and F are not equal sets

∴ E≠F

-------------------------------------------------------

Click the link about "Definition of sets-roster&set builder form-cardinal number"

Sets-1st-class.10-mathematics-introduction-definition of set-roster form-set builder form-belongs to-cardinal number of set

 Mathematics for class 10- Sets-Introduction of Sets

Examine the following statements

1. All Students in your class

2. All States in India

3. Natural numbers greater than three and less than twelve

4. Five good books in your school library

5. Three best singers in India 

First three statements are easy to answer 

But last two statements are difficulty

And any two persons may not give same answers for last two questions

Because first three statements are defined correctly to answer everyone "same"

But not last two statements.

Definition of Set

A Set is a well defined collection of distinct Objects or Numbers or Things or Ideas

Objects in the Set  are called Elements

A Set is said to be well defined,

If we can decide Any object from the universe is an element of the set or not.

Elements of a Set are written inside a pair of curly braces separated by commas.

Elements can’t be repeat in a set 

That means a set contains distinct(different) elements

Example.1:

Vowels in English alphabet.

we can answer easily for this(Why)

Because it is well defined

we write the set

{ a, e, i, o, u }

Example.2:

Prime numbers less than 12.

we can answer easily for this also

Because it is well defined

we write the set

 { 2, 3, 5, 7, 11 }

Note:

A set is named by Capital letters of English alphabet

And

An element is denoted by small letters of English alphabet

Example.3:

A is the set of days which are starts with “T”.

            A = { Tuesday, Thursday }

Example.4:

M is the set of letters in the word “MATHEMATICS”.

            M = { m, a, t, h, e, i, c, s }

Roster form of a set

If a set is written by its

“All elements inside of Flower brackets with using commas”,

 we say that the Set is in “Roster form”

Note: 

No preference is given to Order of elements in a set

Example.5:

A is the Set of days in a week

    

    A= { Sun, Mon, Tue, Wed, Thu, Fri, Sat}

Example.6:

R is the set of Alphabet in the word INDIA

        R= {i, n, d, a }

        or

        R= {a, d, i, n }

Here both sets are equal

not given any priority to the order of elements in the set

Example.7:

P is the set of prime numbers less than 10

        P= { 2, 3, 5, 7 }

Set builder form of a set

If A set is written by “common property” of its elements, we say that the set is in “set builder form”

Note: 

we can write set builder form of a set in "different ways"(Based common property of its elements)

Example.8:

 A = { 2, 4, 6, 8 }

Elements in the set A are "Even numbers"

Even numbers is common property of elements

and Even numbers are less than 10

So we write set builder form as 

A= {x/x is even number and x<10 }

we read this "A is the set of x such that x is even number and x less than 10"

OR

Elements in the set A are "multiples of 2"

"Multiples of 2" is common property of elements

So we write set builder form as

A= { 2x/x is natural number and x<5 }

we read this "A is the set of 2x such that x is natural number and x less than 5"

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Example.9: 

B = { 1, 2, 3, 6 }

Do you know the relation among the elements?

Think  about the relation

All the elements in the set B are " factors of 6"         

"Factors of 6"is the common property of elements

So we write set builder form as

B= {x/x is a factor of 6 }

we read this "B is the set of x such that x is a factor of 6"

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Example.10:

 K = { -1, 0, 1, 2}

Do you know the common property of elements?

Think  about common property

The elements are integers and lie between -2 and 3

"Integers" is the common property

So we write set builder form as

K= {x/x is integer and -1 ≤ x ≤ 2 }

we read this "K is the set of x such that x is an integer and  -1 is  less than or equal to x and x  less than or equal to 2"

Belongs to(∈)

The symbol  “∈” is used for the words “ belongs to ” or “is an element of”

Does not Belongs to(∉)

The symbol “∉” is used for the words “Does not belongs to”or “ is not an element of”

Example.11:

 A = { 1, 3, 7, 8 }

1 is an element in set A

So we say "1 is belongs to A"

We write as

    1 ∈ A

Read as "1 belongs to A"

-----------------------------------

2 is not an element in set A

So we say "2 is not belongs to  set A"

We write as

2 ∉ A

Read as "2 does not belongs to A"

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Cardinal number of a Set

The number of elements in a set is called the Cardinal number of  the Set. 

Cardinal number of  Set A is denoted as n(A). 

Read as "number of A"

Example.12: 

 A = { a, e, i, o, u }

set A has only 5 elements

So

Cardinal number of  Set A is 5

        ∴ n(A) = 5

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Example.13:

 B = { 4, 8, 12 }

Set B has only 3 elements

So

Cardinal number of  Set B is 3

        ∴n(B) = 3          

Click for "worksheet on above concepts"

Click the link for "Types of sets, Basic set operations and Venn diagrams"

Click the link for "Euclid division algorithm&HCF ,  Proof of Irrational number"