EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Relations and Mapping
Grade : ICSE Grade VII
License : Non Commercial Use
Question
1
1.
If A =
{h,s,l}
and B =
{b,d,n}
,
which of the following is relation
R
:
B
→
A
?
(i)
{(h,f),(l,i),(s,o),(h,i),(s,f)}
(ii)
{(s,b),(l,d),(s,d),(h,d),(h,n)}
(iii)
{(n,f),(d,f),(d,i),(d,o),(b,o)}
(iv)
{(b,l),(n,l),(d,l),(d,h),(n,s)}
(v)
{(o,l),(o,s),(i,s),(o,h),(f,l)}
Question
2
2.
Find the cardinality of the given roster form,
where R =
{(1,8),(10,8),(7,3),(1,7),(1,10)}
(i)
6
(ii)
4
(iii)
3
(iv)
5
(v)
7
Question
3
3.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
3
x
2
+
x
+
1
)
and domain of
f
is
{x : -5 ≤ x ≤ -1}
(i)
{71,25,11,3,46}
(ii)
{71,45,11,3,27}
(iii)
{71,45,25,11,1}
(iv)
{71,45,25,11,3}
(v)
{71,45,25,3,10}
Question
4
4.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{10,7,4}
and B =
{1,3,6}
?
(i)
IV
(ii)
I
(iii)
II
(iv)
III
Question
5
5.
If
f
:
A
→
B
is defined by
f
(
x
)
=
(
7
x
+
6
)
and A =
{5,4,8,3}
,
find the range
(i)
{34,62,41}
(ii)
{46,34,62,44}
(iii)
{27,41,34,75}
(iv)
{41,34,62,27}
(v)
{34,-13,41,-12,62,27}
Question
6
6.
Find the domain in the given roster form,
where R =
{(10,8),(1,3),(1,8),(5,7),(5,8)}
(i)
{10,1,5}
(ii)
{10,2,5,1,7}
(iii)
{10,1,5,8}
(iv)
{10,2,5,1}
(v)
{6,8,7,3}
Question
7
7.
If A =
{7,8,10,3}
and B =
{2,5,6}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is less than
b ∈ B
is
(i)
{(3,5),(3,6)}
(ii)
{(3,5),(7,2)}
(iii)
{(3,5),(3,6),(5,3)}
(iv)
{(3,6),(5,3)}
(v)
{(3,5)}
Question
8
8.
If A =
{4,3,6,1,7,2}
and B =
{8,10,1,2,3}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is equal of
b ∈ B
is
(i)
{(3,3),(1,1),(2,2),(6,6)}
(ii)
{(3,3),(1,1),(2,2)}
(iii)
{(3,3),(1,1),(3,1)}
(iv)
{(3,3),(1,1),(2,2),(10,10)}
(v)
{(3,3),(2,2)}
Question
9
9.
If
f
(
x
)
=
(
4
x
+
9
)
, then find
f
(
2
)
(i)
16
(ii)
17
(iii)
14
(iv)
20
(v)
18
Question
10
10.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{3,7,9,5}
and B =
{6,4,2,10,8}
(i)
{(9,8),(7,8),(5,4),(5,6),(9,2)}
(ii)
{}
(iii)
{(9,8),(7,8),(5,4),(7,4),(5,6),(9,2)}
(iv)
{(9,8),(7,8),(7,4),(5,6),(9,2),(4,5)}
(v)
{(9,8),(7,8),(5,4),(7,4),(5,6),(9,2),(4,5)}
Question
11
11.
Which of the following relations is a function
f
:
A
→
B
,
where A =
{g,k,n,e,o}
and B =
{b,o,k,h,n,i}
?
(i)
{(k,h),(e,h),(g,h),(o,n)}
(ii)
{(k,h),(n,o),(g,h),(o,n)}
(iii)
{(k,h),(n,o),(e,h),(g,h),(o,n)}
(iv)
{}
Question
12
12.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{6,5,7,4,10}
and B =
{3,2,1,8}
?
(i)
{(6,8),(7,2),(10,1),(5,8),(4,2)}
(ii)
{(7,8),(10,2),(4,2),(5,3),(6,3)}
(iii)
{(6,8),(5,1),(4,3),(10,8)}
(iv)
{(5,8),(10,1),(7,1),(6,1),(4,3)}
(v)
{(5,8),(4,2),(6,3),(7,1),(10,3)}
Question
13
13.
If A =
{1,10,8}
and B =
{5,2,9}
, then
A ✕ B
is
(i)
II
(ii)
IV
(iii)
III
(iv)
I
Question
14
14.
Find the range of given relation diagram.
(i)
{5,9,2,8}
(ii)
{1,3,6,8}
(iii)
{5,2,9,8,3}
(iv)
{6,1}
(v)
{1,3,6}
Question
15
15.
Find the co-domain of given relation diagram.
(i)
{1,6,5,9}
(ii)
{6,1,5}
(iii)
{1,6,5}
(iv)
{9,7,8,3,6}
(v)
{9,7,8,3}
Question
16
16.
Find the cardinality of the given relation
(i)
4
(ii)
5
(iii)
6
(iv)
8
(v)
7
Question
17
17.
Find the domain of the given relation.
(i)
{6,5,7,10}
(ii)
{9,4,8}
(iii)
{9,2,8,4}
(iv)
{9,2,8,4,6}
(v)
{9,4,8,7}
Question
18
18.
Find the domain and range of the given relation
R
:
A
→
B
=
{(10,2),(10,8),(5,2),(5,8)}
(i)
A = {10,5} , B = {2,8}
(ii)
A = {9,10} , B ={9,5}
(iii)
A = {7,10} , B ={2,16}
(iv)
A = {10,2} , B ={8,10}
(v)
A = {5,10,4} , B ={4,8,2}
Question
19
19.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{8,7,1,10}
and B =
{3,2,9,4}
?
(i)
IV
(ii)
I
(iii)
II
(iv)
III
Question
20
20.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
4
x
−
1
)
and domain of
f
is
{x : 5 ≤ x ≤ 9}
(i)
{19,23,27,31,37}
(ii)
{23,27,31,35,18}
(iii)
{19,27,31,35,24}
(iv)
{19,23,27,31,35}
(v)
{19,23,31,35,25}
Question
21
21.
If A =
{6,10,4,5}
and B =
{9,10,30,12,3,8,7}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a factor of
b ∈ B
is
(i)
{(6,30),(6,12),(10,10),(10,30),(4,12),(4,8),(5,10),(5,30)}
(ii)
{(6,30),(6,12),(10,10),(10,30),(4,8),(5,10),(5,30)}
(iii)
{}
(iv)
{(6,30),(6,12),(10,10),(4,12),(4,8),(5,10),(5,30),(31,9)}
Question
22
22.
If
f
(
x
)
=
(
6
x
+
9
)
and
g
(
y
)
=
(
9
y
+
4
)
, then find
f
(
8
)
,
g
(
2
)
(i)
58,23
(ii)
57,22
(iii)
56,21
(iv)
60,25
(v)
54,19
Question
23
23.
Which of the following relations
R
:
A
→
B
represent a function,
given A =
{7,5,1}
and B =
{8,4,2,9}
?
(i)
IV
(ii)
II
(iii)
I
(iv)
III
Question
24
24.
Let
f
:
R
→
R
be a function defined by given conditions
f
(
x
)
=
(
x
+
6
)
if
x
<
3
f
(
x
)
=
(
x
+
2
)
if
3
≤
x
≤
4
f
(
x
)
=
(
2
x
+
6
)
if
x
>
4
find
f
(
x
)
where x =
7
(i)
13
(ii)
19
(iii)
9
(iv)
20
(v)
21
Question
25
25.
Which of the following statements are true if
f
:
A
→
B
and
a ∈ A
,
b ∈ B
?
a)
f
(
a
)
is called the image of
a
under
f
b)
f
(
b
)
is called the image of
b
under
f
c)
f
(
a
)
=
b
d)
f
(
b
)
=
a
(i)
{a,c}
(ii)
{b,a}
(iii)
{d,c}
(iv)
{b,d,a}
(v)
{b,c,a}
Assignment Key
1) (iv)
2) (iv)
3) (iv)
4) (ii)
5) (iv)
6) (i)
7) (i)
8) (ii)
9) (ii)
10) (iii)
11) (iii)
12) (iii)
13) (iii)
14) (iv)
15) (v)
16) (iii)
17) (ii)
18) (i)
19) (iii)
20) (iv)
21) (i)
22) (ii)
23) (ii)
24) (iv)
25) (i)
