EduSahara™ Assignment
Name : Relations
Chapter : Relations and Mapping
Grade : ICSE Grade VIII
License : Non Commercial Use
Question
1
1.
If A =
{6,9,4}
and B =
{3,5}
, find
A ✕ B
(i)
{(6,3),(6,5),(9,3),(4,3),(4,5),(6,8)}
(ii)
{(6,3),(6,5),(9,3),(9,5),(4,3),(4,5)}
(iii)
{(6,3),(6,5),(9,5),(4,3),(4,5),(3,9)}
(iv)
{(6,3),(6,5),(9,3),(9,5),(4,3),(4,5),(3,9)}
(v)
{(6,3),(6,5),(9,3),(4,3),(4,5)}
Question
2
2.
If A =
{10,2,4}
and B =
{7,3}
, then
A ✕ B
is
(i)
III
(ii)
II
(iii)
I
(iv)
IV
Question
3
3.
If A =
{10,5,2,3}
and B =
{4,7,9}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is less than
b ∈ B
is
(i)
{(5,7),(5,9),(2,4),(2,7),(2,9),(3,4),(3,7),(3,9)}
(ii)
{(5,7),(5,9),(2,4),(2,9),(3,4),(3,7),(3,9),(8,1)}
(iii)
{(5,7),(5,9),(2,4),(2,7),(2,9),(3,4),(3,7),(3,9),(4,2)}
(iv)
{(5,7),(5,9),(2,4),(2,7),(3,4),(3,7),(3,9)}
(v)
{(5,7),(5,9),(2,7),(2,9),(3,4),(3,7),(3,9),(4,2)}
Question
4
4.
If A =
{6,4,3,5}
and B =
{10,2,12,8,7,6}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a factor of
b ∈ B
is
(i)
{(6,12),(6,6),(4,12),(3,12),(3,6),(5,10),(9,3)}
(ii)
{(6,12),(6,6),(4,12),(4,8),(3,12),(3,6),(5,10)}
(iii)
{(6,12),(6,6),(4,12),(3,12),(3,6),(5,10)}
(iv)
{(6,12),(6,6),(4,8),(3,12),(3,6),(5,10),(12,4)}
(v)
{(6,12),(6,6),(4,12),(4,8),(3,12),(3,6),(5,10),(12,4)}
Question
5
5.
If A =
{8,3,9,5,7,6}
and B =
{5,3,9,2,6,7}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is equal of
b ∈ B
is
(i)
{(3,3),(9,9),(5,5),(7,7),(6,6),(2,2)}
(ii)
{(3,3),(9,9),(5,5),(7,7),(6,6),(8,8)}
(iii)
{(3,3),(9,9),(7,7),(6,6)}
(iv)
{(3,3),(9,9),(5,5),(7,7),(6,6)}
(v)
{(3,3),(9,9),(7,7),(6,6),(6,4)}
Question
6
6.
If A =
{6,2,4}
and B =
{9,49,36,4,16,100}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is the square root of
b ∈ B
is
(i)
{(6,36),(2,4),(17,3)}
(ii)
{(6,36),(2,4),(4,16),(4,2)}
(iii)
{(6,36),(4,16),(4,2)}
(iv)
{(6,36),(4,16)}
(v)
{(6,36),(2,4),(4,16)}
Question
7
7.
Find the domain in the given roster form,
where R =
{(10,2),(7,4),(10,4),(10,8),(6,8)}
(i)
{6,1,10,7,9}
(ii)
{10,7,6,8}
(iii)
{4,2,8}
(iv)
{6,1,10,7,9,8}
(v)
{10,7,6}
Question
8
8.
Find the domain of the given relation.
(i)
{6,8,7}
(ii)
{8,6,3}
(iii)
{3,1,5}
(iv)
{6,8,7,3}
(v)
{8,6}
Question
9
9.
Find the co-domain of given relation diagram.
(i)
{10,3,1,9,6}
(ii)
{10,3,1,9}
(iii)
{4,6,8,5}
(iv)
{4,6,8,5,9}
(v)
{1,3,9}
Question
10
10.
Find the range in given roster form,
where R =
{(7,5),(7,10),(8,1),(7,1),(7,4)}
(i)
{5,10,1,4}
(ii)
{7,8,5}
(iii)
{8,3,7}
(iv)
{1,4,10,5,7}
(v)
{1,10,5}
Question
11
11.
Find the range of given relation diagram.
(i)
{2,10,9,3}
(ii)
{6,7,1,8,10}
(iii)
{4,7,1,8,6}
(iv)
{10,5,2,9,3}
(v)
{10,5,2,9,3,6}
Question
12
12.
Find the cardinality of the given roster form,
where R =
{(4,1),(4,5),(4,8),(7,8),(4,4)}
(i)
4
(ii)
8
(iii)
5
(iv)
3
(v)
6
Question
13
13.
Find the cardinality of the given relation
(i)
9
(ii)
8
(iii)
12
(iv)
6
(v)
10
Question
14
14.
If A =
{2,8,14,20,3}
and B =
{7,4,10}
,
then the relation
R
:
A
→
B
such that
a ∈ A
is a multiple of
b ∈ B
is
(i)
{(8,4),(20,4),(20,10),(7,14)}
(ii)
{(8,4),(14,7),(20,4),(20,10),(7,14)}
(iii)
{(8,4),(14,7),(20,10),(5,19)}
(iv)
{(8,4),(14,7),(20,4),(20,10)}
(v)
{(8,4),(14,7),(20,10)}
Question
15
15.
Find the domain and range of the given relation
R
:
A
→
B
=
{(7,5),(7,9),(7,8),(7,2),(3,5),(3,9),(3,8),(3,2),(5,5),(5,9),(5,8),(5,2),(9,5),(9,9),(9,8),(9,2)}
(i)
A = {7,5,3,16} , B ={5,2,8,19}
(ii)
A = {9,3,5} , B ={9,2,8,3}
(iii)
A = {-1,14,2,3} , B ={9,5,0,1}
(iv)
A = {7,3,5,9} , B = {5,9,8,2}
(v)
A = {9,8,5,2,7} , B ={1,2,8,5,9}
Question
16
16.
Write the relation
R
:
A
→
B
in the given diagram,
where A =
{2,7,5,8}
and B =
{6,3,10}
(i)
{(2,10),(2,6),(8,3),(4,4)}
(ii)
{(2,10),(2,6),(8,3)}
(iii)
{(2,10),(2,6),(5,3),(8,3)}
(iv)
{(2,10),(2,6),(5,3),(8,3),(6,2)}
(v)
{(2,10),(5,3),(8,3),(6,2)}
Question
17
17.
If A =
{m,g,f,b}
and B =
{j,p,k,i}
,
which of the following is relation
R
:
A
→
B
?
(i)
{(l,m),(s,m),(q,m),(o,b),(s,b)}
(ii)
{(m,p),(g,j),(g,k),(b,i),(m,j)}
(iii)
{(g,h),(m,l),(f,l),(m,h),(m,o)}
(iv)
{(j,q),(k,l),(i,h),(i,l),(k,h)}
(v)
{(p,f),(i,f),(k,g),(j,m),(j,b)}
Question
18
18.
If A =
{q,f,h,g,a}
and B =
{c,e,i,o,p}
,
which of the following is relation
R
:
B
→
A
?
(i)
{(i,l),(e,r),(o,l),(c,r),(p,l)}
(ii)
{(g,r),(a,r),(f,l),(q,n),(g,n)}
(iii)
{(q,c),(h,c),(a,c),(a,p),(q,o)}
(iv)
{(p,a),(i,a),(p,f),(e,h),(c,a)}
(v)
{(n,g),(r,h),(l,h),(l,a),(n,q)}
Question
19
19.
Which of the following are true?
a)
a
∈
(a,b)
b)
(a,b)
≠
{a,b}
c)
(a,b) = (b,a)
d)
(a,b)
∈
{(a,b)}
e)
(a,b)
⊂
{a,b}
(i)
{e,a,b}
(ii)
{c,d}
(iii)
{a,b}
(iv)
{b,d}
(v)
{c,d,b}
Question
20
20.
If (
(
9
x
+
9
y
+
7
)
,
8
) = (
10
,
(
5
x
+
y
+
8
)
) then find (x,y)
(i)
(
5
12
,
(
-1
12
)
)
(ii)
(
(
-1
12
)
,
1
2
)
(iii)
(
(
-1
12
)
,
5
12
)
(iv)
(
1
12
,
5
12
)
(v)
(
(
-1
14
)
,
5
14
)
Question
21
21.
If n(A) = 1 and n(B) = 4 then the number of possible relations from A → B is
(i)
14
(ii)
16
(iii)
18
(iv)
15
(v)
13
Question
22
22.
Which of the following statements are true if
f
:
A
→
B
and
a ∈ A
,
b ∈ B
?
a)
f
(
a
)
=
b
b)
f
(
b
)
is called the image of
b
under
f
c)
f
(
b
)
=
a
d)
f
(
a
)
is called the image of
a
under
f
(i)
{c,d}
(ii)
{b,d,a}
(iii)
{b,c,a}
(iv)
{b,a}
(v)
{a,d}
Assignment Key
1) (ii)
2) (iii)
3) (i)
4) (ii)
5) (iv)
6) (v)
7) (v)
8) (v)
9) (iii)
10) (i)
11) (i)
12) (iii)
13) (i)
14) (iv)
15) (iv)
16) (iii)
17) (ii)
18) (iv)
19) (iv)
20) (iii)
21) (iv)
22) (v)
