EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Relations and Mapping
Grade : ICSE Grade VII
License : Non Commercial Use
Question
1
1.
If (
(
x
+
y
+
8
)
,
5
) = (
3
,
(
x
+
5
y
+
8
)
) then find (x,y)
(i)
(
(
-9
2
)
,
1
2
)
(ii)
(
(
-11
2
)
,
1
2
)
(iii)
(
(
-11
2
)
,
1
)
(iv)
(
1
2
,
(
-11
2
)
)
(v)
(
(
-21
4
)
,
1
4
)
Question
2
2.
Find the domain of the given relation.
(i)
{9,7,1,4,6}
(ii)
{5,2,10}
(iii)
{2,8,5,10}
(iv)
{5,2,8,10,7}
(v)
{2,8,5,10,4}
Question
3
3.
If
f
(
x
)
=
(
9
x
+
3
)
, then find
f
(
1
)
(i)
9
(ii)
13
(iii)
11
(iv)
12
(v)
15
Question
4
4.
Find the co-domain of given relation diagram.
(i)
{1,8,9,3}
(ii)
{7,2,4,5}
(iii)
{7,2,4,5,9}
(iv)
{3,8,1,9}
(v)
{1,8,9,3,4}
Question
5
5.
Find the range of given relation diagram.
(i)
{1,10,8}
(ii)
{3,9,5,4,7}
(iii)
{3,7,9,4,8}
(iv)
{8,10}
(v)
{8,1,10,9}
Question
6
6.
If A =
{2,6}
and B =
{8,4,10}
, find
A ✕ B
(i)
{(2,8),(2,4),(2,10),(6,4),(6,10),(9,5)}
(ii)
{(2,8),(2,4),(2,10),(6,4),(6,10)}
(iii)
{(2,8),(2,4),(2,10),(6,8),(6,4),(6,10)}
(iv)
{(2,8),(2,4),(6,8),(6,4),(6,10),(10,2)}
(v)
{(2,8),(2,4),(2,10),(6,8),(6,4),(6,10),(10,2)}
Question
7
7.
Find the domain and range of the given relation
R
:
A
→
B
=
{(6,2),(6,7),(1,2),(1,7),(5,2),(5,7)}
(i)
A = {10,6,5,3} , B ={1,5,7}
(ii)
A = {6,1,5} , B = {2,7}
(iii)
A = {5,-6,-2} , B ={1,7}
(iv)
A = {6,9,5} , B ={11,2}
(v)
A = {6,1,2} , B ={2,6}
Question
8
8.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{9,2,8}
and B =
{4,10,3}
(i)
{(2,10),(2,4),(8,3),(2,3),(8,10),(9,4),(9,10),(9,3),(3,8)}
(ii)
{(2,10),(2,4),(8,3),(2,3),(9,4),(9,10),(9,3)}
(iii)
{(2,10),(2,4),(8,3),(8,10),(9,4),(9,10),(9,3),(4,1)}
(iv)
{(2,10),(2,4),(8,3),(2,3),(8,10),(9,4),(9,10),(9,3)}
(v)
{(2,10),(2,4),(2,3),(8,10),(9,4),(9,10),(9,3),(3,8)}
Question
9
9.
Find the range in given roster form,
where R =
{(6,1),(7,9),(3,9),(7,1),(6,5)}
(i)
{1,9,5}
(ii)
{1,5,9,6}
(iii)
{7,6,3}
(iv)
{1,5}
(v)
{6,7,3,9}
Question
10
10.
If A =
{5,2,6}
and B =
{4,9,100,25,36,81}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is the square root of
b ∈ B
is
(i)
{(5,25),(2,4),(6,36),(4,2)}
(ii)
{(5,25),(2,4),(37,5)}
(iii)
{(5,25),(6,36),(4,2)}
(iv)
{(5,25),(6,36)}
(v)
{(5,25),(2,4),(6,36)}
Question
11
11.
If A =
{b,p,s,o,r}
and B =
{f,k,d,e,c}
,
which of the following is relation
R
:
A
→
B
?
(i)
{(g,b),(h,b),(g,p),(g,s),(h,s)}
(ii)
{(f,h),(e,h),(k,h),(f,g),(d,h)}
(iii)
{(c,o),(d,s),(k,r),(d,p),(c,s)}
(iv)
{(s,k),(r,k),(b,f),(o,d),(r,d)}
(v)
{(o,h),(p,g),(r,g),(b,g),(s,g)}
Question
12
12.
Which of the following are true?
a)
(a,b)
⊂
{a,b}
b)
a
∈
(a,b)
c)
(a,b)
≠
{a,b}
d)
(a,b) = (b,a)
e)
(a,b)
∈
{(a,b)}
(i)
{b,e}
(ii)
{c,e}
(iii)
{d,a,c}
(iv)
{b,e,c}
(v)
{a,c}
Question
13
13.
Which of the following relations
R
:
A
→
B
represent a function,
given A =
{9,2,7,3}
and B =
{10,6,8,4}
?
(i)
IV
(ii)
I
(iii)
III
(iv)
II
Question
14
14.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{8,1,6,2,10}
and B =
{7,5,4,3,9}
?
(i)
{(8,5),(6,7),(1,9),(2,7),(10,3)}
(ii)
{(10,4),(2,4),(8,7),(6,3),(1,4)}
(iii)
{(6,7),(1,7),(8,4),(10,3),(2,4)}
(iv)
{(1,3),(8,5),(6,3),(2,9),(10,3)}
(v)
{(2,9),(10,7),(6,7),(1,9),(1,4)}
Question
15
15.
If A =
{5,9}
and B =
{8,3,10}
, then
A ✕ B
is
(i)
I
(ii)
III
(iii)
IV
(iv)
II
Question
16
16.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{8,2,5}
and B =
{1,6,10,7}
?
(i)
III
(ii)
I
(iii)
II
(iv)
IV
Question
17
17.
Which of the following relations is a function given ,
A =
{9,4,2,10,7,3}
and B =
{5,9,4,3,10}
?
(i)
{(9,4),(4,5),(2,5),(7,3),(3,9)}
(ii)
{(9,4),(4,5),(10,4),(7,3),(3,9),(5,2)}
(iii)
{(9,4),(4,5),(2,5),(7,3),(3,9),(5,9)}
(iv)
{(9,4),(4,5),(2,5),(10,4),(7,3),(3,9)}
(v)
{(9,4),(4,5),(2,5),(10,4),(7,3),(3,9),(5,2)}
Question
18
18.
Find the domain in the given roster form,
where R =
{(9,10),(7,1),(7,10),(9,1),(6,10)}
(i)
{9,7,6}
(ii)
{8,7,3,9,6,1}
(iii)
{8,7,3,9,6}
(iv)
{9,7,6,5}
(v)
{10,5,1,4}
Question
19
19.
Which of the following does not represent a function
f
:
A
→
B
,
where A =
{2,5,9,7,3}
and B =
{6,4,8,1}
?
(i)
{(3,1),(7,6),(9,4),(5,4)}
(ii)
{(7,8),(9,4),(3,6),(2,8),(5,8)}
(iii)
{(9,4),(2,1),(3,6),(5,8),(7,8)}
(iv)
{(2,1),(3,1),(9,1),(5,1),(7,1)}
(v)
{(3,1),(9,4),(5,4),(2,4),(7,1)}
Question
20
20.
If A =
{16,12,10,3,6}
and B =
{2,8,4}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a multiple of
b ∈ B
is
(i)
{(16,2),(16,8),(16,4),(12,2),(12,4),(10,2),(6,2)}
(ii)
{(16,2),(16,8),(12,2),(12,4),(10,2),(6,2),(4,16)}
(iii)
{(16,2),(16,8),(16,4),(12,4),(10,2),(6,2)}
(iv)
{(16,2),(16,8),(16,4),(12,2),(12,4),(10,2),(6,2),(4,16)}
(v)
{(16,2),(16,8),(16,4),(12,4),(10,2),(6,2),(3,11)}
Question
21
21.
Which of the following relations is a function
f
:
A
→
B
,
where A =
{i,h,m,o,f,e}
and B =
{j,b,g,l,k}
?
(i)
{(e,k),(h,j),(m,b),(o,g),(f,g),(i,l)}
(ii)
{(e,k),(h,j),(m,b),(f,g),(i,l)}
(iii)
{}
(iv)
{(e,k),(h,j),(m,b),(o,g),(f,g),(i,l),(b,m)}
(v)
{(e,k),(h,j),(o,g),(f,g),(i,l),(b,m)}
Question
22
22.
Which of the following statements are true if
f
:
A
→
B
and
a ∈ A
,
b ∈ B
?
a)
f
(
b
)
=
a
b)
f
(
a
)
=
b
c)
f
(
b
)
is called the image of
b
under
f
d)
f
(
a
)
is called the image of
a
under
f
(i)
{a,b}
(ii)
{b,d}
(iii)
{a,c,b}
(iv)
{a,d,b}
(v)
{c,d}
Question
23
23.
Find the cardinality of the given relation
(i)
9
(ii)
6
(iii)
4
(iv)
7
(v)
5
Question
24
24.
Let
f
:
R
→
R
be a function defined by given conditions
f
(
x
)
=
(
4
x
+
8
)
if
x
<
-8
f
(
x
)
=
(
x
+
7
)
if
-8
≤
x
≤
8
f
(
x
)
=
(
3
x
+
2
)
if
x
>
8
find
f
(
x
)
where x =
5
(i)
13
(ii)
17
(iii)
12
(iv)
11
(v)
28
Question
25
25.
Find the range of
f
:
Z
→
Z
where
f
(
x
)
=
(
2
x
2
+
x
−
5
)
and domain of
f
is
{x : -4 ≤ x ≤ 0}
(i)
{23,10,1,-5}
(ii)
{23,10,1,-4}
(iii)
{23,10,-4,-5,3}
(iv)
{23,10,1,-4,-5}
(v)
{10,1,-4,-5,21}
Assignment Key
1) (ii)
2) (iii)
3) (iv)
4) (ii)
5) (i)
6) (iii)
7) (ii)
8) (iv)
9) (i)
10) (v)
11) (iv)
12) (ii)
13) (ii)
14) (v)
15) (iii)
16) (iv)
17) (iv)
18) (i)
19) (i)
20) (i)
21) (i)
22) (ii)
23) (ii)
24) (iii)
25) (iv)
