NCERT Solutions
Board Paper Solutions
Ask & Answer
School Talk
Login
GET APP
Login
Create Account
Popular
Latest
Expert Answers
ALL
अर्कज
Subject: Maths
, asked on 4/5/18
Example 12
Let N be a set of natural numbers. Define a real valued function.
f
:
N
→
N
b
y
f
(
x
)
=
2
x
+
1
.
U
sin
g
t
h
i
s
d
e
f
i
n
i
t
i
o
n
,
c
o
m
p
l
e
t
e
t
h
e
t
a
b
l
e
g
i
v
e
n
b
e
l
o
w
:
-
x
1
2
3
4
5
6
7
y
f(1) = ......
f(2) = ......
f(3) = ......
f(4) = ......
f(5) = ......
f(6) = ......
f(7) = ......
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Definition 6:
Definition 6
A function which has either R or one of its subsets as its range is called a real valued function. Further, if its domain is also either R or a subset of R, it is called a real function.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain functions and definition 5: A relation f from a set A to a set B is said to be a function if every
element of set A has one and only one image in set B.
Answer
2
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Remarks
A relation R from A to A is also stated as a relation on A.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Q).
Explain note
Note:
The total number of relations that can be defined from a set A to a set B is the number of possible subsets of
A
×
B
. If n(A) = p and n(B) = q, then
n
A
×
B
=
p
q
and the total number of relations is
2
p
q
.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Example 7:
Example 7:-
Let A=, {1,2,3,4,5,6}. Define a relation R from A to A by R={(x,y):y=x+1}
(i) Depict this relation using an arrow diagram.
(ii) Write down the domain, codomain the range of R.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Explain Remarks
Remarks
(i) A relation may be represented algebraically either by the Roster method or by the Set-builder method.
(i) An arrow diagram is a visual representation of a relation.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Meaning of definition 2,3,4
Definition 2
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product AxB. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A X B. The second element is called the image of the first element.
Definition 3
The set of all first elements of the ordered pairs in a relation R from a set A to set B is called the domain of the relation R.
Definition 4
The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range
⊆
codomain.
Answer
1
अर्कज
Subject: Maths
, asked on 4/5/18
Q.10. The Cartesian product A
×
A has 9 elements among which are found (- 1, 0) and (0, 1). Find the set A and the remaining elements of A
×
A.
Answer
1
अर्कज
Subject: Maths
, asked on 3/5/18
L
e
t
P
=
{
-
3
,
-
2
,
-
1
,
0
,
1
,
2
,
3
}
Q
=
1
,
4
3
,
12
7
,
2
,
12
5
,
3
,
4
,
5
,
6
A
r
e
l
a
t
i
o
n
R
f
r
o
m
P
t
o
Q
i
s
d
e
f
i
n
e
d
a
s
R
=
(
x
,
y
)
:
y
=
12
x
+
3
,
x
∈
P
,
y
∈
Q
W
h
a
t
a
r
e
t
h
e
d
o
m
a
i
n
a
n
d
r
a
n
g
e
o
f
r
e
l
a
t
i
o
n
R
r
e
s
p
e
c
t
i
v
e
l
y
?
Answer
1
अर्कज
Subject: Maths
, asked on 3/5/18
Solve this:
Question No. 1
Two finite sets A and B have
λ
a
n
d
μ
elements respectively. The number of elements in the power set of the A is 224 more than the total number of elements in the power set of B. What is the number of relations from A to B?
A.
2
10
B.
2
20
C.
2
30
D.
2
40
Answer
1
Megha
Subject: Maths
, asked on 2/5/18
Solve this:
Q. If A = { - 1, 1}, find
A
×
A
×
A
.
Answer
1
अर्कज ..
Subject: Maths
, asked on 2/5/18
Example 6
Q6. Example 6
. If A × B = {(p, q), (p, r), (m, q), (m, r) , find A and B.
Solution
A = set of first elements = { p, m}
B = set of second elements = {q, r).
Answer
1
अर्कज ..
Subject: Maths
, asked on 2/5/18
Example 4:
Example 4 If P={1,2}, form the set P x P x P.
Solution : we have, P x P x P=[(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)}.
Answer
1
अर्कज ..
Subject: Maths
, asked on 2/5/18
Example 3) Let A={1,2,3}, B={3,4} and C={4,5,6}. Find
(
i
)
A
×
B
∩
C
(
i
i
)
A
×
B
∩
A
×
C
(
i
i
i
)
A
×
B
∪
C
(
i
v
)
A
×
B
∪
A
×
C
Answer
1
Prev
6
7
8
9
10
Next
What are you looking for?
Let N be a set of natural numbers. Define a real valued function.
Definition 6 A function which has either R or one of its subsets as its range is called a real valued function. Further, if its domain is also either R or a subset of R, it is called a real function.
element of set A has one and only one image in set B.
A relation R from A to A is also stated as a relation on A.
Note: The total number of relations that can be defined from a set A to a set B is the number of possible subsets of . If n(A) = p and n(B) = q, then and the total number of relations is .
Example 7:- Let A=, {1,2,3,4,5,6}. Define a relation R from A to A by R={(x,y):y=x+1}
(i) Depict this relation using an arrow diagram.
(ii) Write down the domain, codomain the range of R.
Remarks (i) A relation may be represented algebraically either by the Roster method or by the Set-builder method.
(i) An arrow diagram is a visual representation of a relation.
Definition 2 A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product AxB. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A X B. The second element is called the image of the first element.
Definition 3 The set of all first elements of the ordered pairs in a relation R from a set A to set B is called the domain of the relation R.
Definition 4 The set of all second elements in a relation R from a set A to a set B is called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range codomain.
Question No. 1
Two finite sets A and B have elements respectively. The number of elements in the power set of the A is 224 more than the total number of elements in the power set of B. What is the number of relations from A to B?
A.
B.
C.
D.
Q. If A = { - 1, 1}, find .
Q6. Example 6. If A × B = {(p, q), (p, r), (m, q), (m, r) , find A and B.
Solution A = set of first elements = { p, m}
B = set of second elements = {q, r).
Example 4 If P={1,2}, form the set P x P x P.
Solution : we have, P x P x P=[(1,1,1), (1,1,2), (1,2,1), (1,2,2), (2,1,1), (2,1,2), (2,2,1), (2,2,2)}.