extra questions - sets - everonn - class-11th commerce

7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce

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Question-1

Which of the

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following are

sets?

(i) The

collection ofall months of

a yearbeginning


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with letter J.

(ii) The

collection

of most

talentedwriters of

India.


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(iii) A

team of

eleven best

cricket

batsmen ofthe world.


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(iv) The

collection

of all boys

in your

class. (v) The

collectionof all


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natural

numbers

less than

100.

(vi) Thecollection

of novelswritten by


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the river

Prem

Chand.

(vii)

Thecollection

of all evenintegers.


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(viii)

The

collection

of different

problems inthis

chapter.


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(ix) A

collection

of most

dangerous

animals ofthe world.

Solution:


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Comment

(i), (iv), (v),

(vi), (vii) and

(viii) are

sets.

NIIT Univ


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Avail Scholars

ECE,CSE & BT.Closes on 22n


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Question-2

AB =

{1,2,3,4,5,6,7

,8,9}

A

B {1,2}

and A = {1, 2,

3, 4, 5} find


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the set B.

Solution:

AB = {1, 2,

3, 4, 5, 6, 7, 8,

9}AB = {1,

2} and


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Comment

A = {1, 2, 3,

4, 5}

B = {1, 2,

6, 7, 8, 9}


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Question-3

If U = {1, 2,3, 4, 5, 6, 7,

8, 9}, find thecomplement

s of thefollowing


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sets:

(i) A =

{2, 4, 6, 8}

(ii) B ={1, 3, 5, 7,

9}


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(iii) C =

{ 2, 3, 5, 7}

(iv)

(v) U

Solution:(i) A' = {1, 3,


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5, 7, 9}

(ii) B' = {2, 4,

6, 8}

(iii) C' = {1,

4, 6, 8, 9}(iv) ' = U

(v) U' =


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Comment

Question-4

Let A = {1, 2,3, 4, 5, 6}.

Insert the

appropriate


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symbol

or

in the

blank

spaces:

(i) 5

______ A


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(ii) 8

______ A

(iii) 0

______ A

(iv) 4______A

(v) 2______ A


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(vi) 10

______ A

Solution:

(i) 5 __

__ A

(ii) 8 __

__A


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(iii) 0 __

__ A

(iv) 4 __

__ A

(v) 2 __

__A

(vi) 10 __

__ A


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Comment


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Question-5

If A

B ={2,

3, 4, 5, 6, 8,9, 11}, A

B


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{5,8} and B =

{2, 5, 8, 9}

find the set

A B

Solution:

A

B ={2, 3,4, 5, 6, 8, 9,


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11},

AB =

{5,8}

B = {2, 5, 8,

9}


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Comment

A = {3, 4,

5, 6, 8, 11}

A B =

{3, 4, 6, 11}


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Question-6

If U is the setof all natural

numbers and

A' is the set

of all

composite


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numbers,

what is A?

Solution:

U = {1, 2, 3,4, 5, 6,

.}


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Comment

A' = {4, 6,

..}

Then A = {1,

2, 3, 5,

..}


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Question-7

Write the

followingsets in the

roaster form:

(i) A = {x

: x is an


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integer and

3 x < 7}

(ii) B =

{x : x is a

naturalnumber

less than 6}


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(iii) C =

{x : x is two

digit

natural

numbersuch that

sum of itsdigits is 8}


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(iv) D =

{x : x is a

prime

number

which is adivisor of

60}


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(v) E =

the set of

all letters in

the word

TRIGONOMETRY


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(vi) F =

the set of

all letters in

the word

SETS.

Solution:


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(i) A = {-3, -2,

-1, 0, 1, 2, 3,

4, 5, 6}

(ii) B = {1, 2,3, 4, 5}


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(iii) C = {17,

26, 35, 44,

53, 62, 71}

(iv) D = {2,

3, 5}(v) E = {T, R,

I, G, O, N, M,E, R, Y}


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Comment

(vi) F = {S,

E, T}


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Question-8


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If A = {p, q, r,

s} find A

A

and A

A.

Solution:A = {p, q, r, s}

A

A ={p, q, r, s}


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Comment

AA =

{p, q, r, s}

Question-9Which of the


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following

statements

are true and

which are

false? (i) U' =


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(ii) '

= U

(iii)

For any two

subsets, Xand Y of U,


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(X

Y)' = X'

Y'

(iv)

For any twosubsets, X

and Y of U,


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(X

Y)' = X'

Y'

(v)

For any twosubsets, S

and T of U,


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(S

T)' = S'

T'

(vi)

For any twosubsets S

and T of U,


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(S

T)' = S'

T'

Solution:(i) True

(ii) True(iii) False


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Comment

(iv) False

(v) True

(vi) True

Question-


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10

If A = {x : x is

a letter in theword,

follow} and B = {x : x is

a letter in the

word, wolf},


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show that A

= B.

Solution:

Clearly, A ={f, o , l, w}

and B = {w, o,l, f}.


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Since every

element of A

is in B and

everyelement of B

is in A, so A= B.


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Comment

Question-

11

Express the

following

sets by using


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the set

builder

method:

(i) A = {

1, 3, 5, 7, 9}

(ii) B ={2, 4, 6, 8}


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(iii) C =

{-1, 1}

(iv) D ={1, 5, 10,

15, .}


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(v) E =

{14, 21, 28,

35, 42,

..,98}

Solution:

(i) A = { x : xis an odd


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natural

number, x

9}

(ii) B = { x : xis an even

naturalnumber, x


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8}

(iii) C= {x : x

is an odd

naturalnumber and

|x| < 2}


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(iv) D = {x : x

is a natural

number

multiple of 5

and x = 1}

(v) E = {x : xis a multiple


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Comment

of 7 and

7


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Let U be the

set of all

triangles in a

plane. If A is

the set of alltriangles

with at leastone angle


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different

from 60 ,

what is A?

Solution:U = The set

of alltriangles in a

0


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plane.

A = The set

of all

triangles

with atleast one


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angle

different

from 60 .

A' = The set

of allequilateral

triangles.

0


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Comment

Question-

13List all the

elements of

the following


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sets:

(i) A =

{x : x is an

odd naturalnumber}

(ii) B =


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{x : x is an

integer,

-1/2


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(iv) D =

{x : x is a

letter in the

word"LOYAL"}

(v) E =


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{x : x is a

month of a

year not

having 31

days}

(vi) F ={x : x is a


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consonant in

the English

alphabet

which

precedes k}

Solution:(i) A = {1, 3,


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5, 7, 9, 11,

13.}

(ii) B = {0, 1,

2, 3, 4}

(iii) C = {-2,-1, 1, 2}

(iv) D = {L,O, Y, A}


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(v) E =

{February,

April, June,

September,

November}(vi) F = {b, c,

d, f, g, h, j}


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Comment

Question-

14Represent

the following

sets in a


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Venn

diagram: U =

{2, 3, 5, 7,

11}, A = {2,

3}

Solution:


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Comment

Question-


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15

Match each

of the setson the left

described inthe roster

form with

the same set


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on the right

described in

set builder

form:

(i) {1,

2, 3, 6}(a) { x : x


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is a prime

number and

a divisor of 6

}

(ii) {2,

3}(b) {x : x is


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an odd

natural

number less

than 10}

(iii) {H,

A, Y, R,N} (c)


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{x : x is a

natural

number and

divisor of 6.}

(iv) {1,

3, 5, 7, 9}(d) {x : x is


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a letter of

the word

'HARYANA'.}

Solution:

(i) {1, 2, 3,6} (c)


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{x : x is a

natural

number and

divisor of 6.}

(ii){2,

3}(a) { x : x is


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a prime

number and

a divisor of 6

}

(iii) {H, A, Y,

R, N} (d){x : x is a


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letter of the

word

'HARYANA'.}

(iv) {1, 3, 5, 7,9} (b) {x

: x is an oddnatural


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Comment

number less

than 10}

Question-16


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Which of the

following

sets is finite

or infinite?

(i) The

set of themonths of a


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year.

(ii) {1, 2,

3, }

(iii) {1,2, 3, ..,

99, 100}


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(iv) The

set of

positive

integers

greaterthan 100.

(v) The


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set of prime

numbers

less that

99.

Solution:

(i) Finite set


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(ii) Infinite

set

(iii) Finite

set

(iv) Infiniteset

(v) Finiteset


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Comment

Question-

17Represent

the following

sets in a


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Venn

diagram:

U = { x :

x is a

naturalnumber and

2 x 8.}


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A = {x :

x

U and x

divides 18}

B = {x:

x

U and xis a prime

divisor of18}


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Solution:

U = {2, 3, 4, 5,

6, 7, 8}

A = {2, 3, 6}and B = {2,

3}


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Comment


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Question-

18Which of the

following

sets is finite

or infinte?


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(i) The

set of lines

which are

parallel to

the x-axis. (ii) The

set ofletters in


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the English

alphabet.

(iii)

The set of

numberswhich are

multiples of5.


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(iv)

The set of

animals

living on

earth. (v) The

set ofcircles in


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plane

passing

through the

origin.

Solution:

(i) Infinite set


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(ii) Finite

set

(iii) Infinite

set

(iv) Finiteset

(v) Infiniteset


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Comment

Question-

19If A, B and C

are three

subsets of


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the universal

set U, draw a

venn

diagram

showing A

(B

C)

Solution:


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Comment


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Question-

20Which of the

following are

examples of

the null set?


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(i)

Set of odd

natural

numbers

divisible by2.


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(ii)

Set of even

prime

numbers.

(iii) {x :x is a

naturalnumber,


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x7}

(iv) {y :

y is a pointcommon to

any parallellines}


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Solution:

(i) Null set.

(ii) It is not

a null setbecause 2


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Comment

is a even

prime

number.

(iii) Null set.

(iv) Null set.


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Question-

21

If A, B and Care three

subsets of

the universal

set U, draw a

venn


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diagram

showing (A

B)

C.

Solution:


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Comment

Question-

22

If A, B and Care three


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subsets of

the universal

set U, draw a

venn

diagramshowing [(A

B)

C]'


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Comment

Solution:


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Question-

23In the

following,

state

whether A =

B or not:


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(i) A =

{a, b, c, d}

B = {d, c, b,a}

(ii) A =


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{4, 8, 12,

16}

B = {8, 4,

16, 18}

(iii) A =

{2, 4, 6, 8,10}


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B =

{x :x is

positive even

integer less

than 10}

(iv) A ={x : x is a


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multiple of

10} B =

{10, 15, 20,

25, 30,

.}

Solution:(i) A = B


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(ii) A B,

because

element 12

of set A isnot present

in set B andelement 18


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of set B is

not present

in set A.

(iii) A = B

(iv) A B,because set


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Comment

B consists of

elements

that are

multiple of 5.


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Question-

24If A, B and C

are three

subsets of

the universal

set U, draw a


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venn

diagram

showing (A'

B' )

C'

Solution:


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Comment

Question-


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25

Are the

followingpair of sets

equal? Givereasons.

(i) A ={2, 3}


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B =

{x: x is a

solution of

x + 5x + 6 =

0}

(ii) A ={x:x is a

2


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letter in the

word

FOLLOW}

B =

{y:y is a

letter in the

word WOLF}


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Solution:

(i) A = {2, 3}

B = {x: x is

a solution of

x + 5x + 6 =

0} = {2, 3}

2


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Therefore

the above

pair are

equal sets.

(ii) A = {x:x

is a letter in

the word


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FOLLOW} =

{F, O, L, W}

B = {y:y

is a letter in

the word

WOLF} =

{W, O, L, F}


135/578

Comment

Therefore

the above

pair are

equal sets.


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Question-

26

If A, B, and Care three

subsets of

the universal

set U, draw

Venn


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diagrams for

the

following:B

C, when B

C.

Solution:


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Comment

Question-


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27

From the

sets givenbelow, select

equal setsand

equivalentsets


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A = {0,

a}

B = {1, 2,

3, 4}

C = {4,

8,12}


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D = {3, 1,

2, 4}

E = {1,

0}

F = {8,

4, 12}


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G = {1,

5, 7,

11}

H = {a, b}

Solution:

Equal sets:(i) B = D


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Comment

(ii) C = F;

Equivalent

sets:

(i) A, E, H;

(ii) D, G;


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Question-

28Given that A

= {6, 7, 8, 9,

10} and B =

{2, 3, 4, 5}.

Write down


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all ordered

pairs (a, b)

such that a

is divisible

by b and

hence write

down the setordered pairs


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given the

relation is a

multiple of

from A and

B.

Solution:A = {6, 7, 8, 9,


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10} and B =

{2, 3, 4, 5}

List of all

ordered

pairs : (6,

2), (6, 3), (6,

4), (6, 5), (7,2), (7, 3), (7,


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4), (7, 5), (8,

2), (8, 3), (8,

4), (8, 5), (9,

2), (9, 3), (9,

4), (9, 5),

(10, 2), (10,

3), (10, 4),(10, 5)


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The ordered

pairs (a, b)

such that a

is divisible

by b: (6, 2),

(6, 3), (8, 2),


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Comment

(8, 4), (9, 3),

(10, 2),

(10,5)

Question-


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29

Which of the

followingstatements

are true?

(i) Theset of all


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cats is

contained in

the set of all

animals.

(ii)

The set of

allisosceles


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triangles is

contained

in the set of

all

equilateral

triangles.


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(iii)

The set of

all

rectangles

is

contained

in the set ofall squares.


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(iv)

The sets A

= {1} and B

= {{1}} are

equal.

(v)

The sets A= {x : x is a


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letter in the

word

"TITLE"}

and B = {x :

x is a letter

in the word

"LITTLE"}are equal.


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Solution:

(i) True

(ii) False

(iii) False

(iv) False(v) True


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Comment

Question-

30Let R be the

relation

defined by


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divides"

from A = {2,

3, 5} to B =

{6, 10, 12,

15}.

Represent R

(i) as a set ofordered pairs


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(ii) as a

graph and

(iii) by an

arrow

diagram.

Solution:


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A = {2, 3, 5}

to B = {6,

10, 12, 15}

(i) R = {(2,

6), (2, 10),

(2, 12), (2,

15), (3, 6),(3, 10), (3,


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12), (3, 15),

(5, 6), (5,

10), (5, 12),

(5, 15)}

(ii)


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(iii)


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Comment

Question-

31A and C are

disjoint sets

and both A


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and C are

subsets of B,

draw Venn

diagrams for

the

following.

Solution:


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Comment

Question-


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32

Make correct

statementsby filling in

the symbolsor in the

blankspaces:


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(i) {2,

3, 4} . {1,

2, 3, 4, 5,}

(ii) {a,

b, c}{b,c, d}


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(iii) {x :

x is a

student of

Class 9 of

your school.}

..{x: x is astudent of


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your school}

(iv) {x :x is a circle


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in the plane}

..{x : x is

a circle with

radius 1}

(v) {x :

x is atriangle in


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the plane}

. { x : x

is a

rectangle in

the plane}

(vi) {x :x is an


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equilateral

triangle in

the plane}

.{ x : x is

a triangle in

the plane}

(vii) {x :


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x is an even

natural

number}

{x : x is

an integer}

Solution:(i) {2, 3, 4}


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. {1, 2, 3,

4, 5,}

(ii) {a, b, c}

.. {b, c, d}

(iii) {x : x is astudent of


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Class 9 of

your school.}

.{x; x is

a student of

your school.}

(iv) {x : x is acircle in the


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plane.}

{x : x is a

circle with

radius 1.}

(v) {x : x is a

triangle inthe plane.}


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{ x : x is

a rectangle

in the plane.}

(vi) {x : x is

an

equilateraltriangle in


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the plane .}

{ x : x is

a triangle in

the plane.}

(vii) {x : x is

an evennatural


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Comment

number.}

{x : x is

an integer.}

Question-


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33

If A and B

are two setssuch that A

has 21elements, B

has 17elements,


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and A

B

has 21

elements,

how many

elements

does A

B

have?


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Solution:

We have n(A)

= 12

n(B)

= 17

n(A

B) = 21


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By using

the formula,

n(A

B) = n(A) +

n(B) - n(A

B)


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We have

21 = 12 +

17 - n(A

B)

n(A

B) = 29 -21

n(A

B) = 8


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Comment

Question-

34If P = {2, 3, 4,

8, 9} write

down the


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sets of

ordered pairs

representing

the relations

(i) is a factor

of (ii) is

divisible by(iii) is a


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multiple of 2

on P.

Solution:

P = {2, 3, 4, 8,

9}


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(i) The sets

of ordered

pairs

representin

g "is a

factor of" :

{(2, 2), (2,4), (2, 8), (3,


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3), (3, 9), (4,

4), (4, 8), (8,

8), (9, 9)}

(ii) The sets

of ordered

pairs

representing "is


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divisible by"

: {(2, 2), (4,

2), (8, 2), (4,

4), (8, 4), (8,

8), (9, 3), (9,

9), (3, 3)}


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(iii) The

sets of

ordered

pairs

representin

g "is a

multiple of


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Comment

2 on P" :

{((2, 2), (4,

2)), (8, 2)}

Question-


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35

Examine

whether thefollowing

statementsare true or

false:


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(i) {a,

b}

{b, c, a}

(ii) {a,

e}

{ x : x is

a vowel in

the Englishalphabet.}


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(iii) {1,

2, 3}

{1, 2,

3}

(iv) {a}

{a, b, c}


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(v) {a}

{a, b, c}

(vi) {x :

x is an even

natural

number lessthan 6.}

{


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x : x is a

natural

number

which

divides 36}

Solution:(i) False,


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because

elements a

and b are

present in

that set.

(ii) True


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(iii) True

(iv) True

(v) False

(vi) True


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Comment

Question-

36Describe the

relation R

defined from


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A to B where

A = {- 1, 2, 3,

4} to B = {-2,

4, 6} by the

set R = {(- 1,

- 2), (2, 4),

(3, 6)}.


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Solution:

A = {- 1, 2, 3,

4} to B = {-2,

4, 6}

set R = {(- 1,

- 2), (2, 4),

(3, 6)} is the


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Comment

relation "is

half of"

Question-37


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If A and B

are disjoint

sets, show

that n(A

B) = n(A) +

n(B)

Solution:


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We know

that, if A and

B are disjoint

sets then

n(AB) =

.


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Hence, by

using the

formula n(A

B) = n(A)

+ n(B) - n(A

B)


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We have

n(AB) =

n(A) + n(B) -

n(AB) =

n(A) + n(B)


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Example:

Let A = {1,

2} and B =

{3, 4},

then A

B = {1, 2,

3, 4} and AB =


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Now

n(A) = 2,

n(B) = 2,

n(AB) =

4 and n(A

B) =


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Comment

Hence, n(A

B) = n(A)

+ n(B)

Question-


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38

Let A = {1, 2,

{3, 4}, 5}.Which of the

followingstatements

are false andwhy?


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(i) {3, 4}

A

(ii) {3, 4}

A

(iii) {{3, 4}}


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A

(iv) 1

A

(v) 1

A

(vi) {1, 2, 5}

A


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(vii) {1, 2, 5}

A

(viii) {1, 2, 3}

A

(ix) A


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(x) { }

A

Solution:

(i) False,

{3,4} is anelement not


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a set.

(ii) True

(iii) True

(iv) True

(v) False,

1 is an

element nota set.


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(vi) True

(vii) False,

{1, 2, 5} is a

set not an

element.

(viii) False,

3 is anelement of


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set

contained

in A.

(ix) False,

is not an

element of

A.


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Comment

(x) False,

is not an

element of

A.


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Question-

39Write the

power set of

A = {3,6,9}.

Solution:


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Comment

P(A)= {, {3},

{9},{6},{3,6},

{3,9},{6,9},

{3,6,9}}.


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Question-

40Describe the

relation,

domain and

range if (i) R

= {(1, 1), (8,


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2), (27, 3),

(64, 4)} (ii) R

= {(Delhi,

India),

(Paris,

France),

(Karachi,Pakistan)}


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(iii) R = {(4, -

2), (9, - 3),

(1, 1), (4, 2),

(1, - 1), (9,

3)}

Solution:(i) R = {(1, 1),


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(8, 2), (27, 3),

(64, 4)}

R is the

relation "is

the cube of

"

Domain ={1, 8, 27, 64}


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Range = {1,

2, 3, 4}

(ii) R =

{(Delhi,

India),

(Paris,


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France),

(Karachi,

Pakistan)}

R is the

relation "is

the capital

of"


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Domain =

{Delhi,

Paris,

Karachi}

Range =

{India ,

France,Pakistan}


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(iii) R = {(4, -

2), (9, - 3),

(1, 1), (4, 2),

(1, - 1), (9,

3)}

R is the

relation "isthe square


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Comment

of"

Domain =

{1, 4, 9}

Range = (-

3, - 2, - 1, 2 ,

3}


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Question-

41If x

{1, 3,

7}, y{0, 2,

8} and R is

the relation

such that x +


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y < 8,

represent R

(i) as a set of

ordered pairs

and (ii) by an

arrow

diagram.


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Solution:

(i) x{1, 3,

7}, y{0, 2,

8} , R is such

that x + y

extra questions - sets - everonn - class-11th commerce

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