EduSahara™ Assignment
Name : Concepts
Chapter : Relations and Mapping
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
If A =
{9,5,4}
and B =
{7,6,8,2}
, find
A ✕ B
(i)
{(9,7),(9,6),(9,8),(9,2),(5,7),(5,8),(5,2),(4,7),(4,6),(4,8),(4,2),(7,4)}
(ii)
{(9,7),(9,6),(9,8),(9,2),(5,7),(5,6),(5,2),(4,7),(4,6),(4,8),(4,2)}
(iii)
{(9,7),(9,6),(9,8),(9,2),(5,7),(5,6),(5,8),(5,2),(4,7),(4,6),(4,8),(4,2)}
(iv)
{(9,7),(9,6),(9,8),(9,2),(5,6),(5,8),(5,2),(4,7),(4,6),(4,8),(4,2),(7,5)}
(v)
{(9,7),(9,6),(9,8),(9,2),(5,7),(5,6),(5,8),(5,2),(4,7),(4,6),(4,8),(4,2),(7,5)}
Question
2
2.
If A =
{1,6}
and B =
{5,4,3}
, then
A ✕ B
is
(i)
III
(ii)
I
(iii)
II
(iv)
IV
Question
3
3.
If A =
{10,8,3,5}
and B =
{2,7,4}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is less than
b ∈ B
is
(i)
{(3,7),(3,4),(8,4)}
(ii)
{(3,7),(5,7)}
(iii)
{(3,7),(3,4),(5,7),(4,3)}
(iv)
{(3,7),(5,7),(4,3)}
(v)
{(3,7),(3,4),(5,7)}
Question
4
4.
If A =
{2,7,10,9}
and B =
{5,28,8,27,4,20,6}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a factor of
b ∈ B
is
(i)
{(2,28),(2,8),(2,20),(2,6),(7,28),(10,20),(9,27),(4,2)}
(ii)
{(2,28),(2,8),(2,4),(2,20),(2,6),(7,28),(10,20),(9,27)}
(iii)
{(2,28),(2,8),(2,4),(2,20),(7,28),(10,20),(9,27)}
(iv)
{(2,28),(2,8),(2,4),(2,6),(7,28),(10,20),(9,27),(21,1)}
(v)
{(2,28),(2,8),(2,4),(2,20),(2,6),(7,28),(10,20),(9,27),(4,2)}
Question
5
5.
If A =
{3,1,6,9,4,2}
and B =
{8,2,6,5,7,4}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is equal of
b ∈ B
is
(i)
{(6,6),(4,4),(2,2)}
(ii)
{(6,6),(4,4),(2,2),(8,8)}
(iii)
{(6,6),(4,4),(3,1)}
(iv)
{(6,6),(2,2)}
(v)
{(6,6),(4,4),(2,2),(9,9)}
Question
6
6.
If A =
{3,7,9}
and B =
{81,16,49,64,25,9}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is the square root of
b ∈ B
is
(i)
{(3,9),(7,49),(82,8)}
(ii)
{(3,9),(7,49),(9,81)}
(iii)
{(3,9),(9,81)}
(iv)
{(3,9),(9,81),(49,7)}
(v)
{(3,9),(7,49),(9,81),(49,7)}
Question
7
7.
Find the domain in the given roster form,
where R =
{(3,8),(6,8),(4,8),(5,8),(6,7)}
(i)
{3,6,4,5}
(ii)
{4,3,10,6,5}
(iii)
{9,1,2,7,8}
(iv)
{3,6,4,5,7}
(v)
{4,3,10,6,5,1}
Question
8
8.
Find the domain of the given relation.
(i)
{9,10,2}
(ii)
{9,6,3,10,2,4}
(iii)
{9,10,2,7}
(iv)
{9,6,3,10,2}
(v)
{1,5,4,8,7}
Question
9
9.
Find the co-domain of given relation diagram.
(i)
{3,6,5,9}
(ii)
{3,6,5}
(iii)
{9,1,10,2,7,6}
(iv)
{9,1,10,2,7}
(v)
{7,9,2,1,10}
Question
10
10.
Find the range in given roster form,
where R =
{(6,5),(6,4),(9,1),(9,2),(6,1)}
(i)
{1,5,2}
(ii)
{5,4,1,2}
(iii)
{1,5,2,4,8}
(iv)
{6,9,1}
(v)
{9,6,8}
Question
11
11.
Find the range of given relation diagram.
(i)
{5,2}
(ii)
{7,6,2}
(iii)
{7,6,3}
(iv)
{2,1,5}
(v)
{5,1,2,3}
Question
12
12.
Find the cardinality of the given roster form,
where R =
{(4,4),(6,10),(8,5),(4,10),(6,5)}
(i)
6
(ii)
4
(iii)
2
(iv)
5
(v)
7
Question
13
13.
If A =
{12,36,8,10,7}
and B =
{9,5,3}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a multiple of
b ∈ B
is
(i)
{(12,3),(36,3),(10,5),(9,36)}
(ii)
{(12,3),(36,9),(10,5)}
(iii)
{(12,3),(36,9),(36,3),(10,5)}
(iv)
{(12,3),(36,9),(36,3),(10,5),(9,36)}
(v)
{(12,3),(36,9),(10,5),(4,35)}
Question
14
14.
If R is a relation from
A→B
,
where A =
{4,5,7}
and B =
{9,2,8}
, find
R
⁻¹
.
(i)
{(8,4),(2,7),(9,5),(8,7),(2,5),(9,4),(8,8)}
(ii)
{(8,4),(2,7),(9,7),(8,7),(2,5),(9,4),(5,9)}
(iii)
{(8,4),(2,7),(9,5),(8,7),(2,5),(9,4)}
(iv)
{(8,4),(2,7),(9,5),(9,7),(8,7),(2,5),(9,4)}
(v)
{(8,4),(2,7),(9,5),(9,7),(8,7),(2,5),(9,4),(5,9)}
Question
15
15.
If A =
{5,3,4,1}
and B =
{3,7,4,5,6}
,
find the roster form of the relation
R
:
A
→
B
shown in the diagram
(i)
{}
(ii)
{(1,6),(5,5),(3,4),(4,5)}
(iii)
{(1,6),(5,5),(5,4),(3,4),(4,5)}
Question
16
16.
If A =
{h,q,o}
and B =
{i,l,k}
,
which of the following is relation
R
:
A
→
B
?
(i)
{(i,q),(i,o),(k,h),(l,q),(l,o)}
(ii)
{(i,s),(k,d),(l,r),(l,d),(i,c)}
(iii)
{(q,k),(o,i),(h,l),(h,i),(q,l)}
(iv)
{(h,g),(h,r),(o,d),(q,c),(q,d)}
(v)
{(g,h),(c,o),(d,h),(s,q),(d,q)}
Question
17
17.
Find the domain from the given graphical representation of relation R.
(i)
{6,4,1,2,3,7}
(ii)
{6,4,1,2,3}
(iii)
{5,7,8}
(iv)
{3,1,2,4,7}
(v)
{3,1,2,4}
Question
18
18.
Find the range from the given graphical representation of relation R.
(i)
{1,4,8}
(ii)
{3,5,7,8}
(iii)
{2,6,8,7,5,3}
(iv)
{2,6,8,7,5,3,4}
(v)
{1,4}
Question
19
19.
Which of the following are true?
a)
(a,b)
⊂
{a,b}
b)
(a,b)
≠
{a,b}
c)
(a,b) = (b,a)
d)
(a,b)
∈
{(a,b)}
e)
a
∈
(a,b)
(i)
{e,a,b}
(ii)
{c,d}
(iii)
{a,b}
(iv)
{c,d,b}
(v)
{b,d}
Question
20
20.
If n(A) = 1 and n(B) = 3 then the number of possible relations from A → B is
(i)
5
(ii)
7
(iii)
10
(iv)
6
(v)
8
Question
21
21.
If A =
{2,9,1}
and B =
{3,4,6}
, find
(A ✕ B)
⁻¹
(i)
{(2,3),(2,4),(2,6),(9,3),(9,4),(9,6),(1,3),(1,4),(1,6)}
(ii)
{}
(iii)
{(3,2),(4,2),(6,2),(3,9),(4,9),(6,9),(3,1),(4,1),(6,1)}
(iv)
{(3,2),(4,2),(6,2),(3,9),(6,9),(3,1),(4,1),(6,1),(10,3)}
Question
22
22.
Find the cardinality of the given relation
(i)
3
(ii)
6
(iii)
5
(iv)
7
(v)
8
Question
23
23.
Find the domain and range of the given relation
R
:
A
→
B
=
{(1,1),(1,2),(1,3),(1,4),(4,1),(4,2),(4,3),(4,4),(9,1),(9,2),(9,3),(9,4),(8,1),(8,2),(8,3),(8,4)}
(i)
A = {1,4,9,8} , B = {1,2,3,4}
(ii)
A = {8,4,1,2} , B ={2,3,4}
(iii)
A = {8,4,7,1,9} , B ={8,3,5,4,1}
(iv)
A = {15,6,1,8} , B ={8,1,-5,6}
(v)
A = {8,12,9,1} , B ={2,10,4,3}
Question
24
24.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{9,4,3,2,10}
and B =
{6,5,8,7}
(i)
{(4,6),(3,8),(4,5),(7,3)}
(ii)
{(4,6),(3,7),(4,5)}
(iii)
{(4,6),(3,7),(3,8),(4,5),(7,3)}
(iv)
{(4,6),(3,7),(3,8),(4,5)}
(v)
{(4,6),(3,7),(4,5),(9,2)}
Question
25
25.
If
f
(
x
)
=
(
5
x
+
8
)
, then find
f
(
3
)
(i)
20
(ii)
24
(iii)
23
(iv)
25
(v)
22
Question
26
26.
If
f
(
x
)
=
(
3
x
+
9
)
and
g
(
y
)
=
(
9
y
+
4
)
, then find
f
(
6
)
,
g
(
8
)
(i)
28,77
(ii)
30,79
(iii)
25,74
(iv)
27,76
(v)
26,75
Question
27
27.
If
f
:
A
→
B
is defined by
f
(
x
)
=
(
5
x
+
2
)
and A =
{8,3,5,7}
,
find the range
(i)
{17,27,37}
(ii)
{20,42,16,37}
(iii)
{42,17,27,37}
(iv)
{17,27,-3,37,-6,42}
(v)
{17,37,34,42}
Question
28
28.
If A =
{p,e,m}
and B =
{j,l,s}
,
which of the following is relation
R
:
B
→
A
?
(i)
{(l,m),(j,p),(s,e),(s,p),(j,e)}
(ii)
{(l,r),(j,a),(j,r),(j,n),(l,a)}
(iii)
{(d,m),(n,p),(k,m),(r,e),(d,p)}
(iv)
{(p,n),(m,k),(m,d),(p,g),(m,n)}
(v)
{(p,s),(m,j),(p,j),(e,s),(m,l)}
Question
29
29.
Find the domain of
R
⁻¹
where
R =
{(1,9),(1,6),(1,2),(8,2),(7,3)}
(i)
{9,6,2,3,4}
(ii)
{6,9,2,4}
(iii)
{9,6,2,3}
(iv)
{8,1,4}
(v)
{8,1,7,4}
Question
30
30.
Find the domain of
R
⁻¹
from the given diagram.
(i)
{3,7,8,1}
(ii)
{4,9,6,2}
(iii)
{4,9,5,6,2}
(iv)
{8,3,1,7,2}
(v)
{3,7,8,1,4}
Question
31
31.
Find the range of
R
⁻¹
where
R =
{(5,7),(4,3),(5,10),(6,10),(6,7)}
(i)
{5,4,6}
(ii)
{10,3,7,1,8}
(iii)
{10,3,7,1}
(iv)
{6,5,9,1}
Question
32
32.
Find the range of
R
⁻¹
from the given diagram.
(i)
{2}
(ii)
{2,3}
(iii)
{1,10,8,4}
(iv)
{5,3,2,1}
(v)
{1,10,8,7,4}
Question
33
33.
Find
R
⁻¹
given R =
{(7,3),(10,7),(5,7),(3,7),(10,3)}
(i)
{(3,7),(7,10),(7,5),(3,10)}
(ii)
{(3,7),(7,3),(7,10),(7,5),(3,10)}
(iii)
{}
(iv)
{(3,7),(7,3),(7,5),(3,10)}
(v)
{(3,7),(7,3),(7,5),(3,10),(11,6)}
Question
34
34.
If (
(
8
x
+
7
y
+
4
)
,
2
) = (
7
,
(
8
x
+
3
y
+
6
)
) then find (x,y)
(i)
(
(
-35
32
)
,
7
4
)
(ii)
(
(
-37
32
)
,
7
4
)
(iii)
(
7
4
,
(
-37
32
)
)
(iv)
(
(
-37
32
)
,
5
2
)
(v)
(
(
-39
34
)
,
3
2
)
Assignment Key
1) (iii)
2) (ii)
3) (v)
4) (ii)
5) (i)
6) (ii)
7) (i)
8) (i)
9) (ii)
10) (ii)
11) (iv)
12) (iv)
13) (iii)
14) (iv)
15) (iii)
16) (iii)
17) (v)
18) (v)
19) (v)
20) (ii)
21) (iii)
22) (ii)
23) (i)
24) (iv)
25) (iii)
26) (iv)
27) (iii)
28) (i)
29) (iii)
30) (i)
31) (i)
32) (ii)
33) (ii)
34) (ii)
