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. 

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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!

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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"

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

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"

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

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"

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

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

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

Example.13:

 B = { 4, 8, 12 }

Set B has only 3 elements

So

Cardinal number of  Set B is 3

        ∴n(B) = 3          

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