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"

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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.

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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

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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

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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

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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

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