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अर्कज ..
Subject: Maths
, asked on 22/4/18
Solve this:
Question No. 1
A survey of 120 people in a particular locality shows that 80 people own bikes and 45 people own bikes but not cars. If each person owns at least one of the two vehicles, then what is the number of people who own a car but not a bike?
A) 60
B) 50
C) 40
D) 30
Answer
6
Uma
Subject: Maths
, asked on 21/4/18
Prove that A - (B U C) = (A - B) ∩ (A - C)
Answer
1
अर्कज ..
Subject: Maths
, asked on 21/4/18
Ques.
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subset of A x B having 3 or more elements is
A) 256
B) 220
C) 219
D) 211
Answer
2
अर्कज ..
Subject: Maths
, asked on 21/4/18
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e
t
A
a
n
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B
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.
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A
×
B
,
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v
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s
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s
:
A
)
219
B
)
256
C
)
275
D
)
510
Answer
2
अर्कज ..
Subject: Maths
, asked on 21/4/18
Q Let S = (1, 2, 3,...9). For k = 1, 2,...5, let
N
k
be the number of subsets of S, each containing five elements
out of which exactly k are odd. Then
N
1
+
N
2
+
N
3
+
N
4
+
N
5
A) 125
B) 252
C) 210
D) 126
Q. Q Let
S
=
x
∈
R
:
x
≥
0
a
n
d
2
x
-
3
+
x
x
-
6
+
6
=
0
.
. Then S
A) contains exactly two elements
8) contains exactly four elements.
C) is an empty set
D) contains exactly one element.
Answer
2
Utkarsh
Subject: Maths
, asked on 20/4/18
derive the formula of n(P(A))=2
n
Answer
1
अर्कज ..
Subject: Maths
, asked on 20/4/18
Theorem 2
Theorem 2 If A,B and C are any three sets,then prove that:
i
A
-
B
∩
C
=
A
-
B
∪
A
-
C
(
ii
)
A
-
(
B
∪
C
)
=
A
-
B
∩
A
-
C
(
iii
)
A
∩
B
-
C
=
A
∩
B
-
(
A
∩
C
)
(
iv
)
A
∩
B
△
C
=
A
∩
B
△
A
∩
C
Answer
1
अर्कज ..
Subject: Maths
, asked on 20/4/18
Theorem 1
THEOREM 1 If A and B are any two sets,then
i
A
-
B
=
A
∩
B
'
(
ii
)
B
-
A
=
B
∩
A
'
(
iii
)
A
-
B
=
A
⇔
A
∩
B
=
ϕ
(
iv
)
(
A
-
B
)
∪
B
=
A
∪
B
(
v
)
A
-
B
∩
B
=
ϕ
(
vi
)
A
⊆
B
⇔
B
'
⊆
A
'
(
vii
)
(
A
-
B
)
∪
(
B
-
A
)
=
(
A
∪
B
)
-
(
A
∩
B
)
Answer
1
अर्कज
Subject: Maths
, asked on 20/4/18
Illustration 2 and note
Answer
1
अर्कज
Subject: Maths
, asked on 20/4/18
Union of sets . What is proved there ?
Answer
1
अर्कज
Subject: Maths
, asked on 20/4/18
Difference between proper and improper subsets . Does the same apply for super sets . And any others ?
Answer
1
अर्कज
Subject: Maths
, asked on 20/4/18
Prove that A is a subset of phi implies A=phi
Answer
1
अर्कज
Subject: Maths
, asked on 20/4/18
Example 2 3 4 5
Answer
1
Tanya Shankar
Subject: Maths
, asked on 20/4/18
For any two sets a and b prove that a union b =a intersection b
Answer
1
Keta
Subject: Maths
, asked on 18/4/18
In this question are the places of A and B in venn diagram marked correctly or else the ones marked in red are correct? Pls answer..
Example 6:
Given set A = (x x is a natural number less than 10} and set B = {y: y is an even number less than 9}. Is set B a subset of set A? If yes then draw the Venn-diagram depicting the given sets.
Solution:
Given, A = (x, x is a natural number less than 10)
i.e A= {1,2,3,4,5,6,7,8,9,}
B = {y. y is an even number less than 9)
i.e., B={2,4,6,8,}
It is clear that B
⊂
A.
Venn-diagram for B
⊂
A is shown below:
Answer
3
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Question No. 1
A survey of 120 people in a particular locality shows that 80 people own bikes and 45 people own bikes but not cars. If each person owns at least one of the two vehicles, then what is the number of people who own a car but not a bike?
A) 60
B) 50
C) 40
D) 30
A) 256
B) 220
C) 219
D) 211
out of which exactly k are odd. Then
A) 125
B) 252
C) 210
D) 126
Q. Q Let . Then S
A) contains exactly two elements
8) contains exactly four elements.
C) is an empty set
D) contains exactly one element.
Theorem 2 If A,B and C are any three sets,then prove that:
THEOREM 1 If A and B are any two sets,then
Example 6:
Given set A = (x x is a natural number less than 10} and set B = {y: y is an even number less than 9}. Is set B a subset of set A? If yes then draw the Venn-diagram depicting the given sets.
Solution:
Given, A = (x, x is a natural number less than 10)
i.e A= {1,2,3,4,5,6,7,8,9,}
B = {y. y is an even number less than 9)
i.e., B={2,4,6,8,}
It is clear that B A.
Venn-diagram for BA is shown below: