EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Relations and Mapping
Grade : ICSE Grade VII
License : Non Commercial Use
Question
1
1.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{2,6,3,8,7}
and B =
{1,4,10,5,9}
?
(i)
{(8,4),(6,1),(2,9),(3,5),(7,4)}
(ii)
{(8,4),(3,4),(6,5),(7,1)}
(iii)
{(7,9),(3,10),(2,10),(6,10),(8,4)}
(iv)
{(8,5),(7,5),(6,5),(3,5),(2,10)}
(v)
{(7,4),(2,5),(8,1),(6,5),(3,10)}
Question
2
2.
Find the range in given roster form,
where R =
{(2,4),(5,4),(6,9),(8,1),(5,9)}
(i)
{4,9,1}
(ii)
{4,1}
(iii)
{2,5,6,8,9}
(iv)
{4,1,9,5}
(v)
{8,10,6,2,5}
Question
3
3.
If A =
{5,9,7,2}
and B =
{4,6}
, find
A ✕ B
(i)
{(5,4),(5,6),(9,4),(7,4),(7,6),(2,4),(2,6),(7,8)}
(ii)
{(5,4),(5,6),(9,4),(9,6),(7,4),(7,6),(2,4),(2,6)}
(iii)
{(5,4),(5,6),(9,6),(7,4),(7,6),(2,4),(2,6),(4,9)}
(iv)
{(5,4),(5,6),(9,4),(9,6),(7,4),(7,6),(2,4),(2,6),(4,9)}
(v)
{(5,4),(5,6),(9,4),(9,6),(7,6),(2,4),(2,6)}
Question
4
4.
Find the domain of the given relation.
(i)
{10,5,9}
(ii)
{1,3,6,10}
(iii)
{1,3,6}
(iv)
{8,3,6,1,2,10}
(v)
{8,3,6,1,2}
Question
5
5.
If A =
{6,10,2}
and B =
{36,4,9,25,81,100}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is the square root of
b ∈ B
is
(i)
{(6,36),(2,4),(100,10)}
(ii)
{(6,36),(10,100),(2,4)}
(iii)
{(6,36),(10,100),(2,4),(100,10)}
(iv)
{(6,36),(10,100),(5,1)}
(v)
{(6,36),(2,4)}
Question
6
6.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
2
x
2
+
2
x
+
6
)
and domain of
f
is
{x : 0 ≤ x ≤ 4}
(i)
{6,10,18,30,46}
(ii)
{6,18,30,46,11}
(iii)
{10,18,30,46,4}
(iv)
{6,10,30,46,20}
(v)
{6,10,18,30,45}
Question
7
7.
Find the domain and range of the given relation
R
:
A
→
B
=
{(1,9),(1,8),(1,1),(7,9),(7,8),(7,1),(8,9),(8,8),(8,1),(4,9),(4,8),(4,1)}
(i)
A = {1,7,8,4} , B = {9,8,1}
(ii)
A = {8,1,7} , B ={1,8,7}
(iii)
A = {4,7,8,3} , B ={9,1,17}
(iv)
A = {5,1,4,25} , B ={4,8,5}
(v)
A = {8,10,3,4,7} , B ={8,9,5,1}
Question
8
8.
If A =
{5,7,10,9,6,2}
and B =
{2,10,5,6,9}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is equal of
b ∈ B
is
(i)
{(5,5),(10,10),(6,6),(2,2)}
(ii)
{(5,5),(10,10),(9,9),(6,6),(2,2),(0,0)}
(iii)
{(5,5),(10,10),(9,9),(6,6),(2,2),(7,7)}
(iv)
{(5,5),(10,10),(9,9),(6,6),(2,2)}
(v)
{(5,5),(10,10),(6,6),(2,2),(10,8)}
Question
9
9.
If
f
(
x
)
=
(
6
x
+
4
)
, then find
f
(
9
)
(i)
58
(ii)
57
(iii)
59
(iv)
61
(v)
56
Question
10
10.
If
f
:
A
→
B
is defined by
f
(
x
)
=
(
x
+
6
)
and A =
{5,4,7,1}
,
find the range
(i)
{20,11,10,13}
(ii)
{10,-11,13,-1,11,7}
(iii)
{11,10,13,7}
(iv)
{15,25,11,9}
(v)
{7,10,13}
Question
11
11.
Let
f
:
R
→
R
be a function defined by given conditions
f
(
x
)
=
(
6
x
+
7
)
if
x
<
-1
f
(
x
)
=
(
2
x
+
8
)
if
-1
≤
x
≤
5
f
(
x
)
=
(
7
x
+
8
)
if
x
>
5
find
f
(
x
)
where x =
-4
(i)
-20
(ii)
0
(iii)
-17
(iv)
-16
(v)
-18
Question
12
12.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{9,3,10,2,1,8}
and B =
{5,7,4,6}
?
(i)
{(10,7),(9,5),(2,7),(8,7),(1,4),(3,7)}
(ii)
{(8,4),(2,6),(9,7),(1,6),(10,7),(1,5)}
(iii)
{(1,7),(2,7),(3,7),(10,5),(9,4),(8,6)}
(iv)
{(1,6),(8,4),(9,5),(10,7),(3,4),(2,4)}
(v)
{(2,5),(3,4),(8,4),(1,7),(10,5),(9,7)}
Question
13
13.
If A =
{m,o,p,e}
and B =
{h,f,s,l}
,
which of the following is relation
R
:
B
→
A
?
(i)
{(l,j),(f,g),(f,n),(f,j),(h,j)}
(ii)
{(p,g),(p,q),(m,g),(m,j),(o,n)}
(iii)
{(g,p),(n,o),(j,o),(j,p),(g,e)}
(iv)
{(m,l),(o,f),(p,l),(o,l),(e,l)}
(v)
{(f,e),(h,e),(s,e),(f,o),(l,p)}
Question
14
14.
Which of the following relations
R
:
A
→
B
represent a function,
given A =
{6,3}
and B =
{7,1,5}
?
(i)
II
(ii)
III
(iii)
I
(iv)
IV
Question
15
15.
If (
(
5
x
+
7
y
+
2
)
,
3
) = (
4
,
(
5
x
+
9
y
+
2
)
) then find (x,y)
(i)
(
11
10
,
-1
)
(ii)
(
13
12
,
(
-1
4
)
)
(iii)
(
13
10
,
(
-1
2
)
)
(iv)
(
11
10
,
(
-1
2
)
)
(v)
(
(
-1
2
)
,
11
10
)
Question
16
16.
Find the domain in the given roster form,
where R =
{(2,5),(2,4),(2,7),(9,7),(1,4)}
(i)
{2,9,1}
(ii)
{7,3,4,6,5}
(iii)
{9,10,1,2}
(iv)
{2,9,1,5}
(v)
{9,10,1,2,3}
Question
17
17.
If A =
{2,3}
and B =
{10,9}
, then
A ✕ B
is
(i)
II
(ii)
IV
(iii)
I
(iv)
III
Question
18
18.
Find the cardinality of the given relation
(i)
3
(ii)
5
(iii)
6
(iv)
8
(v)
7
Question
19
19.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{10,8,7,4,3}
and B =
{2,9,5,6}
(i)
{(4,6),(4,9),(10,2),(3,2),(10,6),(8,5),(7,2)}
(ii)
{}
(iii)
{(4,6),(4,9),(10,2),(3,2),(3,6),(10,6),(8,5),(7,2)}
(iv)
{(4,6),(4,9),(3,2),(3,6),(10,6),(8,5),(7,2),(2,10)}
(v)
{(4,6),(4,9),(10,2),(3,2),(3,6),(10,6),(8,5),(7,2),(2,10)}
Question
20
20.
Which of the following relations does not represent a function
f
:
A
→
B
,
where A =
{a,d,f,o,j,h}
and B =
{k,n,i,b,m,l}
?
(i)
{(j,i),(a,m),(d,m),(f,k),(o,m),(h,b)}
(ii)
{(d,k),(h,b),(j,i),(o,n),(d,n),(j,n)}
(iii)
{(a,m),(j,i),(d,n),(o,k),(h,l),(f,k)}
(iv)
{(h,i),(j,m),(d,l),(a,n),(o,k),(f,i)}
(v)
{(d,m),(f,n),(j,m),(h,l),(o,m),(a,n)}
Question
21
21.
Which of the following statements are true if
f
:
A
→
B
and
a ∈ A
,
b ∈ B
?
a)
f
(
b
)
=
a
b)
f
(
a
)
is called the image of
a
under
f
c)
f
(
a
)
=
b
d)
f
(
b
)
is called the image of
b
under
f
(i)
{a,c,b}
(ii)
{b,c}
(iii)
{a,b}
(iv)
{a,d,b}
(v)
{d,c}
Question
22
22.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{6,9,10}
and B =
{2,5,4}
?
(i)
I
(ii)
III
(iii)
II
(iv)
IV
Question
23
23.
Which of the following are true?
a)
(a,b)
≠
{a,b}
b)
(a,b) = (b,a)
c)
a
∈
(a,b)
d)
(a,b)
∈
{(a,b)}
e)
(a,b)
⊂
{a,b}
(i)
{e,b,a}
(ii)
{b,a}
(iii)
{c,d}
(iv)
{c,d,a}
(v)
{a,d}
Question
24
24.
Find the cardinality of the given roster form,
where R =
{(9,8),(5,3),(5,7),(7,7),(7,6),(6,8),(7,3),(5,6),(7,8),(6,7)}
(i)
9
(ii)
12
(iii)
10
(iv)
7
(v)
11
Question
25
25.
If A =
{5,3,16,27,20}
and B =
{10,4,9}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a multiple of
b ∈ B
is
(i)
{(16,4),(20,10),(20,4),(9,27)}
(ii)
{(16,4),(27,9),(20,10),(20,4)}
(iii)
{(16,4),(27,9),(20,10),(20,4),(9,27)}
(iv)
{(16,4),(27,9),(20,4),(11,19)}
(v)
{(16,4),(27,9),(20,4)}
Assignment Key
1) (ii)
2) (i)
3) (ii)
4) (iii)
5) (ii)
6) (i)
7) (i)
8) (iv)
9) (i)
10) (iii)
11) (iii)
12) (ii)
13) (v)
14) (ii)
15) (iv)
16) (i)
17) (ii)
18) (iii)
19) (iii)
20) (ii)
21) (ii)
22) (iv)
23) (v)
24) (iii)
25) (ii)
