extra questions - sets - everonn - class-11th commerce
TRANSCRIPT
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
1/578
Android AppInstall Now!
No. 1 Android App for Ex
Preparation
(http://ad.apsalar.cre=0&st=93675793
http://gradestack.com/mainsite/explorecoursehttp://ad.apsalar.com/api/v1/ad?re=0&st=936757937694&h=999d72d9570c57c682fc966dfbc9e3ccca2a1b9ehttp://ad.apsalar.com/api/v1/ad?re=0&st=936757937694&h=999d72d9570c57c682fc966dfbc9e3ccca2a1b9ehttp://ad.apsalar.com/api/v1/ad?re=0&st=936757937694&h=999d72d9570c57c682fc966dfbc9e3ccca2a1b9ehttp://gradestack.com/mainsite/explorecoursehttp://ad.apsalar.com/api/v1/ad?re=0&st=936757937694&h=999d72d9570c57c682fc966dfbc9e3ccca2a1b9e -
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
2/578
Question-1
Which of the
Math tuLearn - Practise -Test
http://gradestack.com/web/registerhttp://gradestack.com/mainsite/explorecoursehttp://gradestack.com/web/loginhttp://gradestack.com/web/register -
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
3/578
following are
sets?
(i) The
collection ofall months of
a yearbeginning
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
4/578
with letter J.
(ii) The
collection
of most
talentedwriters of
India.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
5/578
(iii) A
team of
eleven best
cricket
batsmen ofthe world.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
6/578
(iv) The
collection
of all boys
in your
class. (v) The
collectionof all
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
7/578
natural
numbers
less than
100.
(vi) Thecollection
of novelswritten by
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
8/578
the river
Prem
Chand.
(vii)
Thecollection
of all evenintegers.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
9/578
(viii)
The
collection
of different
problems inthis
chapter.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
10/578
(ix) A
collection
of most
dangerous
animals ofthe world.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
11/578
Comment
(i), (iv), (v),
(vi), (vii) and
(viii) are
sets.
NIIT Univ
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
12/578
Avail Scholars
ECE,CSE & BT.Closes on 22n
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
13/578
Question-2
AB =
{1,2,3,4,5,6,7
,8,9}
A
B {1,2}
and A = {1, 2,
3, 4, 5} find
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
14/578
the set B.
Solution:
AB = {1, 2,
3, 4, 5, 6, 7, 8,
9}AB = {1,
2} and
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
15/578
Comment
A = {1, 2, 3,
4, 5}
B = {1, 2,
6, 7, 8, 9}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
16/578
Question-3
If U = {1, 2,3, 4, 5, 6, 7,
8, 9}, find thecomplement
s of thefollowing
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
17/578
sets:
(i) A =
{2, 4, 6, 8}
(ii) B ={1, 3, 5, 7,
9}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
18/578
(iii) C =
{ 2, 3, 5, 7}
(iv)
(v) U
Solution:(i) A' = {1, 3,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
19/578
5, 7, 9}
(ii) B' = {2, 4,
6, 8}
(iii) C' = {1,
4, 6, 8, 9}(iv) ' = U
(v) U' =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
20/578
Comment
Question-4
Let A = {1, 2,3, 4, 5, 6}.
Insert the
appropriate
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
21/578
symbol
or
in the
blank
spaces:
(i) 5
______ A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
22/578
(ii) 8
______ A
(iii) 0
______ A
(iv) 4______A
(v) 2______ A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
23/578
(vi) 10
______ A
Solution:
(i) 5 __
__ A
(ii) 8 __
__A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
24/578
(iii) 0 __
__ A
(iv) 4 __
__ A
(v) 2 __
__A
(vi) 10 __
__ A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
25/578
Comment
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
26/578
Question-5
If A
B ={2,
3, 4, 5, 6, 8,9, 11}, A
B
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
27/578
{5,8} and B =
{2, 5, 8, 9}
find the set
A B
Solution:
A
B ={2, 3,4, 5, 6, 8, 9,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
28/578
11},
AB =
{5,8}
B = {2, 5, 8,
9}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
29/578
Comment
A = {3, 4,
5, 6, 8, 11}
A B =
{3, 4, 6, 11}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
30/578
Question-6
If U is the setof all natural
numbers and
A' is the set
of all
composite
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
31/578
numbers,
what is A?
Solution:
U = {1, 2, 3,4, 5, 6,
.}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
32/578
Comment
A' = {4, 6,
..}
Then A = {1,
2, 3, 5,
..}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
33/578
Question-7
Write the
followingsets in the
roaster form:
(i) A = {x
: x is an
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
34/578
integer and
3 x < 7}
(ii) B =
{x : x is a
naturalnumber
less than 6}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
35/578
(iii) C =
{x : x is two
digit
natural
numbersuch that
sum of itsdigits is 8}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
36/578
(iv) D =
{x : x is a
prime
number
which is adivisor of
60}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
37/578
(v) E =
the set of
all letters in
the word
TRIGONOMETRY
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
38/578
(vi) F =
the set of
all letters in
the word
SETS.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
39/578
(i) A = {-3, -2,
-1, 0, 1, 2, 3,
4, 5, 6}
(ii) B = {1, 2,3, 4, 5}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
40/578
(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}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
41/578
Comment
(vi) F = {S,
E, T}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
42/578
Question-8
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
43/578
If A = {p, q, r,
s} find A
A
and A
A.
Solution:A = {p, q, r, s}
A
A ={p, q, r, s}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
44/578
Comment
AA =
{p, q, r, s}
Question-9Which of the
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
45/578
following
statements
are true and
which are
false? (i) U' =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
46/578
(ii) '
= U
(iii)
For any two
subsets, Xand Y of U,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
47/578
(X
Y)' = X'
Y'
(iv)
For any twosubsets, X
and Y of U,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
48/578
(X
Y)' = X'
Y'
(v)
For any twosubsets, S
and T of U,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
49/578
(S
T)' = S'
T'
(vi)
For any twosubsets S
and T of U,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
50/578
(S
T)' = S'
T'
Solution:(i) True
(ii) True(iii) False
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
51/578
Comment
(iv) False
(v) True
(vi) True
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
52/578
10
If A = {x : x is
a letter in theword,
follow} and B = {x : x is
a letter in the
word, wolf},
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
53/578
show that A
= B.
Solution:
Clearly, A ={f, o , l, w}
and B = {w, o,l, f}.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
54/578
Since every
element of A
is in B and
everyelement of B
is in A, so A= B.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
55/578
Comment
Question-
11
Express the
following
sets by using
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
56/578
the set
builder
method:
(i) A = {
1, 3, 5, 7, 9}
(ii) B ={2, 4, 6, 8}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
57/578
(iii) C =
{-1, 1}
(iv) D ={1, 5, 10,
15, .}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
58/578
(v) E =
{14, 21, 28,
35, 42,
..,98}
Solution:
(i) A = { x : xis an odd
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
59/578
natural
number, x
9}
(ii) B = { x : xis an even
naturalnumber, x
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
60/578
8}
(iii) C= {x : x
is an odd
naturalnumber and
|x| < 2}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
61/578
(iv) D = {x : x
is a natural
number
multiple of 5
and x = 1}
(v) E = {x : xis a multiple
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
62/578
Comment
of 7 and
7
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
63/578
Let U be the
set of all
triangles in a
plane. If A is
the set of alltriangles
with at leastone angle
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
64/578
different
from 60 ,
what is A?
Solution:U = The set
of alltriangles in a
0
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
65/578
plane.
A = The set
of all
triangles
with atleast one
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
66/578
angle
different
from 60 .
A' = The set
of allequilateral
triangles.
0
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
67/578
Comment
Question-
13List all the
elements of
the following
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
68/578
sets:
(i) A =
{x : x is an
odd naturalnumber}
(ii) B =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
69/578
{x : x is an
integer,
-1/2
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
70/578
(iv) D =
{x : x is a
letter in the
word"LOYAL"}
(v) E =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
71/578
{x : x is a
month of a
year not
having 31
days}
(vi) F ={x : x is a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
72/578
consonant in
the English
alphabet
which
precedes k}
Solution:(i) A = {1, 3,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
73/578
5, 7, 9, 11,
13.}
(ii) B = {0, 1,
2, 3, 4}
(iii) C = {-2,-1, 1, 2}
(iv) D = {L,O, Y, A}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
74/578
(v) E =
{February,
April, June,
September,
November}(vi) F = {b, c,
d, f, g, h, j}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
75/578
Comment
Question-
14Represent
the following
sets in a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
76/578
Venn
diagram: U =
{2, 3, 5, 7,
11}, A = {2,
3}
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
77/578
Comment
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
78/578
15
Match each
of the setson the left
described inthe roster
form with
the same set
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
79/578
on the right
described in
set builder
form:
(i) {1,
2, 3, 6}(a) { x : x
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
80/578
is a prime
number and
a divisor of 6
}
(ii) {2,
3}(b) {x : x is
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
81/578
an odd
natural
number less
than 10}
(iii) {H,
A, Y, R,N} (c)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
82/578
{x : x is a
natural
number and
divisor of 6.}
(iv) {1,
3, 5, 7, 9}(d) {x : x is
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
83/578
a letter of
the word
'HARYANA'.}
Solution:
(i) {1, 2, 3,6} (c)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
84/578
{x : x is a
natural
number and
divisor of 6.}
(ii){2,
3}(a) { x : x is
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
85/578
a prime
number and
a divisor of 6
}
(iii) {H, A, Y,
R, N} (d){x : x is a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
86/578
letter of the
word
'HARYANA'.}
(iv) {1, 3, 5, 7,9} (b) {x
: x is an oddnatural
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
87/578
Comment
number less
than 10}
Question-16
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
88/578
Which of the
following
sets is finite
or infinite?
(i) The
set of themonths of a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
89/578
year.
(ii) {1, 2,
3, }
(iii) {1,2, 3, ..,
99, 100}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
90/578
(iv) The
set of
positive
integers
greaterthan 100.
(v) The
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
91/578
set of prime
numbers
less that
99.
Solution:
(i) Finite set
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
92/578
(ii) Infinite
set
(iii) Finite
set
(iv) Infiniteset
(v) Finiteset
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
93/578
Comment
Question-
17Represent
the following
sets in a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
94/578
Venn
diagram:
U = { x :
x is a
naturalnumber and
2 x 8.}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
95/578
A = {x :
x
U and x
divides 18}
B = {x:
x
U and xis a prime
divisor of18}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
96/578
Solution:
U = {2, 3, 4, 5,
6, 7, 8}
A = {2, 3, 6}and B = {2,
3}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
97/578
Comment
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
98/578
Question-
18Which of the
following
sets is finite
or infinte?
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
99/578
(i) The
set of lines
which are
parallel to
the x-axis. (ii) The
set ofletters in
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
100/578
the English
alphabet.
(iii)
The set of
numberswhich are
multiples of5.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
101/578
(iv)
The set of
animals
living on
earth. (v) The
set ofcircles in
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
102/578
plane
passing
through the
origin.
Solution:
(i) Infinite set
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
103/578
(ii) Finite
set
(iii) Infinite
set
(iv) Finiteset
(v) Infiniteset
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
104/578
Comment
Question-
19If A, B and C
are three
subsets of
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
105/578
the universal
set U, draw a
venn
diagram
showing A
(B
C)
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
106/578
Comment
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
107/578
Question-
20Which of the
following are
examples of
the null set?
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
108/578
(i)
Set of odd
natural
numbers
divisible by2.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
109/578
(ii)
Set of even
prime
numbers.
(iii) {x :x is a
naturalnumber,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
110/578
x7}
(iv) {y :
y is a pointcommon to
any parallellines}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
111/578
Solution:
(i) Null set.
(ii) It is not
a null setbecause 2
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
112/578
Comment
is a even
prime
number.
(iii) Null set.
(iv) Null set.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
113/578
Question-
21
If A, B and Care three
subsets of
the universal
set U, draw a
venn
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
114/578
diagram
showing (A
B)
C.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
115/578
Comment
Question-
22
If A, B and Care three
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
116/578
subsets of
the universal
set U, draw a
venn
diagramshowing [(A
B)
C]'
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
117/578
Comment
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
118/578
Question-
23In the
following,
state
whether A =
B or not:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
119/578
(i) A =
{a, b, c, d}
B = {d, c, b,a}
(ii) A =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
120/578
{4, 8, 12,
16}
B = {8, 4,
16, 18}
(iii) A =
{2, 4, 6, 8,10}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
121/578
B =
{x :x is
positive even
integer less
than 10}
(iv) A ={x : x is a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
122/578
multiple of
10} B =
{10, 15, 20,
25, 30,
.}
Solution:(i) A = B
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
123/578
(ii) A B,
because
element 12
of set A isnot present
in set B andelement 18
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
124/578
of set B is
not present
in set A.
(iii) A = B
(iv) A B,because set
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
125/578
Comment
B consists of
elements
that are
multiple of 5.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
126/578
Question-
24If A, B and C
are three
subsets of
the universal
set U, draw a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
127/578
venn
diagram
showing (A'
B' )
C'
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
128/578
Comment
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
129/578
25
Are the
followingpair of sets
equal? Givereasons.
(i) A ={2, 3}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
130/578
B =
{x: x is a
solution of
x + 5x + 6 =
0}
(ii) A ={x:x is a
2
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
131/578
letter in the
word
FOLLOW}
B =
{y:y is a
letter in the
word WOLF}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
132/578
Solution:
(i) A = {2, 3}
B = {x: x is
a solution of
x + 5x + 6 =
0} = {2, 3}
2
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
133/578
Therefore
the above
pair are
equal sets.
(ii) A = {x:x
is a letter in
the word
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
134/578
FOLLOW} =
{F, O, L, W}
B = {y:y
is a letter in
the word
WOLF} =
{W, O, L, F}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
135/578
Comment
Therefore
the above
pair are
equal sets.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
136/578
Question-
26
If A, B, and Care three
subsets of
the universal
set U, draw
Venn
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
137/578
diagrams for
the
following:B
C, when B
C.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
138/578
Comment
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
139/578
27
From the
sets givenbelow, select
equal setsand
equivalentsets
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
140/578
A = {0,
a}
B = {1, 2,
3, 4}
C = {4,
8,12}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
141/578
D = {3, 1,
2, 4}
E = {1,
0}
F = {8,
4, 12}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
142/578
G = {1,
5, 7,
11}
H = {a, b}
Solution:
Equal sets:(i) B = D
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
143/578
Comment
(ii) C = F;
Equivalent
sets:
(i) A, E, H;
(ii) D, G;
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
144/578
Question-
28Given that A
= {6, 7, 8, 9,
10} and B =
{2, 3, 4, 5}.
Write down
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
145/578
all ordered
pairs (a, b)
such that a
is divisible
by b and
hence write
down the setordered pairs
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
146/578
given the
relation is a
multiple of
from A and
B.
Solution:A = {6, 7, 8, 9,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
147/578
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,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
148/578
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)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
149/578
The ordered
pairs (a, b)
such that a
is divisible
by b: (6, 2),
(6, 3), (8, 2),
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
150/578
Comment
(8, 4), (9, 3),
(10, 2),
(10,5)
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
151/578
29
Which of the
followingstatements
are true?
(i) Theset of all
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
152/578
cats is
contained in
the set of all
animals.
(ii)
The set of
allisosceles
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
153/578
triangles is
contained
in the set of
all
equilateral
triangles.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
154/578
(iii)
The set of
all
rectangles
is
contained
in the set ofall squares.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
155/578
(iv)
The sets A
= {1} and B
= {{1}} are
equal.
(v)
The sets A= {x : x is a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
156/578
letter in the
word
"TITLE"}
and B = {x :
x is a letter
in the word
"LITTLE"}are equal.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
157/578
Solution:
(i) True
(ii) False
(iii) False
(iv) False(v) True
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
158/578
Comment
Question-
30Let R be the
relation
defined by
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
159/578
divides"
from A = {2,
3, 5} to B =
{6, 10, 12,
15}.
Represent R
(i) as a set ofordered pairs
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
160/578
(ii) as a
graph and
(iii) by an
arrow
diagram.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
161/578
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,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
162/578
12), (3, 15),
(5, 6), (5,
10), (5, 12),
(5, 15)}
(ii)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
163/578
(iii)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
164/578
Comment
Question-
31A and C are
disjoint sets
and both A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
165/578
and C are
subsets of B,
draw Venn
diagrams for
the
following.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
166/578
Comment
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
167/578
32
Make correct
statementsby filling in
the symbolsor in the
blankspaces:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
168/578
(i) {2,
3, 4} . {1,
2, 3, 4, 5,}
(ii) {a,
b, c}{b,c, d}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
169/578
(iii) {x :
x is a
student of
Class 9 of
your school.}
..{x: x is astudent of
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
170/578
your school}
(iv) {x :x is a circle
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
171/578
in the plane}
..{x : x is
a circle with
radius 1}
(v) {x :
x is atriangle in
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
172/578
the plane}
. { x : x
is a
rectangle in
the plane}
(vi) {x :x is an
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
173/578
equilateral
triangle in
the plane}
.{ x : x is
a triangle in
the plane}
(vii) {x :
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
174/578
x is an even
natural
number}
{x : x is
an integer}
Solution:(i) {2, 3, 4}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
175/578
. {1, 2, 3,
4, 5,}
(ii) {a, b, c}
.. {b, c, d}
(iii) {x : x is astudent of
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
176/578
Class 9 of
your school.}
.{x; x is
a student of
your school.}
(iv) {x : x is acircle in the
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
177/578
plane.}
{x : x is a
circle with
radius 1.}
(v) {x : x is a
triangle inthe plane.}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
178/578
{ x : x is
a rectangle
in the plane.}
(vi) {x : x is
an
equilateraltriangle in
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
179/578
the plane .}
{ x : x is
a triangle in
the plane.}
(vii) {x : x is
an evennatural
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
180/578
Comment
number.}
{x : x is
an integer.}
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
181/578
33
If A and B
are two setssuch that A
has 21elements, B
has 17elements,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
182/578
and A
B
has 21
elements,
how many
elements
does A
B
have?
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
183/578
Solution:
We have n(A)
= 12
n(B)
= 17
n(A
B) = 21
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
184/578
By using
the formula,
n(A
B) = n(A) +
n(B) - n(A
B)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
185/578
We have
21 = 12 +
17 - n(A
B)
n(A
B) = 29 -21
n(A
B) = 8
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
186/578
Comment
Question-
34If P = {2, 3, 4,
8, 9} write
down the
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
187/578
sets of
ordered pairs
representing
the relations
(i) is a factor
of (ii) is
divisible by(iii) is a
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
188/578
multiple of 2
on P.
Solution:
P = {2, 3, 4, 8,
9}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
189/578
(i) The sets
of ordered
pairs
representin
g "is a
factor of" :
{(2, 2), (2,4), (2, 8), (3,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
190/578
3), (3, 9), (4,
4), (4, 8), (8,
8), (9, 9)}
(ii) The sets
of ordered
pairs
representing "is
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
191/578
divisible by"
: {(2, 2), (4,
2), (8, 2), (4,
4), (8, 4), (8,
8), (9, 3), (9,
9), (3, 3)}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
192/578
(iii) The
sets of
ordered
pairs
representin
g "is a
multiple of
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
193/578
Comment
2 on P" :
{((2, 2), (4,
2)), (8, 2)}
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
194/578
35
Examine
whether thefollowing
statementsare true or
false:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
195/578
(i) {a,
b}
{b, c, a}
(ii) {a,
e}
{ x : x is
a vowel in
the Englishalphabet.}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
196/578
(iii) {1,
2, 3}
{1, 2,
3}
(iv) {a}
{a, b, c}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
197/578
(v) {a}
{a, b, c}
(vi) {x :
x is an even
natural
number lessthan 6.}
{
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
198/578
x : x is a
natural
number
which
divides 36}
Solution:(i) False,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
199/578
because
elements a
and b are
present in
that set.
(ii) True
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
200/578
(iii) True
(iv) True
(v) False
(vi) True
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
201/578
Comment
Question-
36Describe the
relation R
defined from
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
202/578
A to B where
A = {- 1, 2, 3,
4} to B = {-2,
4, 6} by the
set R = {(- 1,
- 2), (2, 4),
(3, 6)}.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
203/578
Solution:
A = {- 1, 2, 3,
4} to B = {-2,
4, 6}
set R = {(- 1,
- 2), (2, 4),
(3, 6)} is the
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
204/578
Comment
relation "is
half of"
Question-37
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
205/578
If A and B
are disjoint
sets, show
that n(A
B) = n(A) +
n(B)
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
206/578
We know
that, if A and
B are disjoint
sets then
n(AB) =
.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
207/578
Hence, by
using the
formula n(A
B) = n(A)
+ n(B) - n(A
B)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
208/578
We have
n(AB) =
n(A) + n(B) -
n(AB) =
n(A) + n(B)
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
209/578
Example:
Let A = {1,
2} and B =
{3, 4},
then A
B = {1, 2,
3, 4} and AB =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
210/578
Now
n(A) = 2,
n(B) = 2,
n(AB) =
4 and n(A
B) =
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
211/578
Comment
Hence, n(A
B) = n(A)
+ n(B)
Question-
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
212/578
38
Let A = {1, 2,
{3, 4}, 5}.Which of the
followingstatements
are false andwhy?
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
213/578
(i) {3, 4}
A
(ii) {3, 4}
A
(iii) {{3, 4}}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
214/578
A
(iv) 1
A
(v) 1
A
(vi) {1, 2, 5}
A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
215/578
(vii) {1, 2, 5}
A
(viii) {1, 2, 3}
A
(ix) A
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
216/578
(x) { }
A
Solution:
(i) False,
{3,4} is anelement not
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
217/578
a set.
(ii) True
(iii) True
(iv) True
(v) False,
1 is an
element nota set.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
218/578
(vi) True
(vii) False,
{1, 2, 5} is a
set not an
element.
(viii) False,
3 is anelement of
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
219/578
set
contained
in A.
(ix) False,
is not an
element of
A.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
220/578
Comment
(x) False,
is not an
element of
A.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
221/578
Question-
39Write the
power set of
A = {3,6,9}.
Solution:
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
222/578
Comment
P(A)= {, {3},
{9},{6},{3,6},
{3,9},{6,9},
{3,6,9}}.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
223/578
Question-
40Describe the
relation,
domain and
range if (i) R
= {(1, 1), (8,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
224/578
2), (27, 3),
(64, 4)} (ii) R
= {(Delhi,
India),
(Paris,
France),
(Karachi,Pakistan)}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
225/578
(iii) R = {(4, -
2), (9, - 3),
(1, 1), (4, 2),
(1, - 1), (9,
3)}
Solution:(i) R = {(1, 1),
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
226/578
(8, 2), (27, 3),
(64, 4)}
R is the
relation "is
the cube of
"
Domain ={1, 8, 27, 64}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
227/578
Range = {1,
2, 3, 4}
(ii) R =
{(Delhi,
India),
(Paris,
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
228/578
France),
(Karachi,
Pakistan)}
R is the
relation "is
the capital
of"
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
229/578
Domain =
{Delhi,
Paris,
Karachi}
Range =
{India ,
France,Pakistan}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
230/578
(iii) R = {(4, -
2), (9, - 3),
(1, 1), (4, 2),
(1, - 1), (9,
3)}
R is the
relation "isthe square
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
231/578
Comment
of"
Domain =
{1, 4, 9}
Range = (-
3, - 2, - 1, 2 ,
3}
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
232/578
Question-
41If x
{1, 3,
7}, y{0, 2,
8} and R is
the relation
such that x +
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
233/578
y < 8,
represent R
(i) as a set of
ordered pairs
and (ii) by an
arrow
diagram.
-
7/26/2019 Extra Questions - Sets - Everonn - Class-11th Commerce
234/578
Solution:
(i) x{1, 3,
7}, y{0, 2,
8} , R is such
that x + y