EduSahara™ Worksheet

Question 1

1.

(i)

{(6,3),(6,10),(6,2),(6,8),(1,3),(1,10),(1,8),(9,3),(9,10),(9,2),(9,8),(7,3),(7,10),(7,2),(7,8),(3,0)}
(ii)

{(6,3),(6,10),(6,2),(6,8),(1,3),(1,10),(1,2),(1,8),(9,10),(9,2),(9,8),(7,3),(7,10),(7,2),(7,8)}
(iii)

{(6,3),(6,10),(6,2),(6,8),(1,3),(1,10),(1,2),(1,8),(9,3),(9,10),(9,2),(9,8),(7,3),(7,10),(7,2),(7,8)}
(iv)

{(6,3),(6,10),(6,2),(6,8),(1,3),(1,2),(1,8),(9,3),(9,10),(9,2),(9,8),(7,3),(7,10),(7,2),(7,8),(10,1)}
(v)

{(6,3),(6,10),(6,2),(6,8),(1,3),(1,10),(1,2),(1,8),(9,3),(9,10),(9,2),(9,8),(7,3),(7,10),(7,2),(7,8),(10,1)}

Question 2

2.

(i)

I
(ii)

IV
(iii)

II
(iv)

III

Question 3

3.

If A =
{7,5,2,6}
and B =
{10,3,9}
,

(i)

{(7,10),(7,9),(5,10),(2,10),(2,3),(2,9),(6,10),(6,9),(9,5)}
(ii)

{(7,10),(7,9),(5,10),(5,9),(2,3),(2,9),(6,10),(6,9),(11,1)}
(iii)

{(7,10),(7,9),(5,10),(5,9),(2,10),(2,3),(2,9),(6,10),(6,9),(9,5)}
(iv)

{(7,10),(7,9),(5,10),(5,9),(2,3),(2,9),(6,10),(6,9)}
(v)

{(7,10),(7,9),(5,10),(5,9),(2,10),(2,3),(2,9),(6,10),(6,9)}

Question 4

4.

If A =
{7,8,6,3}
and B =
{14,12,4,32,2,5,9,18}
,

(i)

{(7,14),(8,32),(6,18),(3,12),(3,9),(3,18),(12,6)}
(ii)

{(7,14),(8,32),(6,12),(6,18),(3,12),(3,9),(3,18)}
(iii)

{(7,14),(8,32),(6,12),(6,18),(3,12),(3,9),(3,18),(12,6)}
(iv)

{(7,14),(8,32),(6,12),(3,12),(3,9),(3,18)}
(v)

{(7,14),(8,32),(6,12),(3,12),(3,9),(3,18),(19,5)}

Question 5

5.

If A =
{9,10,1,4,5,3}
and B =
{1,10,3,5,9,4}
,

(i)

{(9,9),(10,10),(1,1),(4,4),(3,3),(6,4)}
(ii)

{(9,9),(10,10),(1,1),(5,5),(4,4),(3,3)}
(iii)

{(9,9),(10,10),(1,1),(4,4),(3,3)}
(iv)

{(9,9),(10,10),(1,1),(5,5),(4,4),(3,3),(0,0)}

Question 6

6.

If A =
{4,2,3}
and B =
{64,16,9,25,100,4}
,

(i)

{(4,16),(2,4),(10,2)}
(ii)

{(4,16),(2,4),(3,9)}
(iii)

{(4,16),(3,9),(4,2)}
(iv)

{(4,16),(3,9)}
(v)

{(4,16),(2,4),(3,9),(4,2)}

Question 7

7.

Find the domain in the given roster form,

where R =
{(7,3),(9,8),(2,3),(1,8),(7,6)}

(i)

{7,2,9,1,8}
(ii)

{7,2,1}
(iii)

{7,9,2,1}
(iv)

{7,9,2,1,8}
(v)

{3,6,8}

Question 8

8.

Find the domain of the given relation.

(i)

{5,10,9,6}
(ii)

{5,10,9,6,4}
(iii)

{6,10,1,9,5,7}
(iv)

{3,2,7,4}
(v)

{6,10,1,9,5}

Question 9

9.

Find the co-domain of given relation diagram.

(i)

{8,6,4,2}
(ii)

{1,5,2,9,8}
(iii)

{2,5,1}
(iv)

{1,5,2,9}
(v)

{8,6,4}

Question 10

10.

Find the range in given roster form,

where R =
{(8,9),(3,9),(5,9),(3,10),(1,9)}

(i)

{6,9,10,1}
(ii)

{9,10}
(iii)

{6,9,10}
(iv)

{1,7,5,3,8}
(v)

{8,3,5,1,10}

Question 11

11.

Find the range of given relation diagram.

(i)

{2,4,10,6,8}
(ii)

{2,4,10,6}
(iii)

{8,1,3}
(iv)

{6,4,2}
(v)

{1,8,3,10}

Question 12

12.

Find the cardinality of the given roster form,

where R =
{(8,7),(5,4),(5,2),(5,8),(9,7),(9,6),(3,8)}

(i)

6
(ii)

4
(iii)

7
(iv)

8
(v)

10

Question 13

13.

If A =
{27,4,12,5,7}
and B =
{4,2,9}
,

(i)

{(27,9),(4,4),(4,2),(12,4),(12,2)}
(ii)

{(27,9),(4,4),(12,4),(12,2),(3,3)}
(iii)

{(27,9),(4,4),(12,4),(12,2)}
(iv)

{}

Question 14

14.

If R is a relation from
A→B
,

(i)

{(6,8),(7,3),(1,3),(7,8),(10,8),(1,4),(3,1)}
(ii)

{(6,8),(7,3),(7,8),(10,8),(1,4),(3,1)}
(iii)

{(6,8),(7,3),(1,3),(10,8),(1,4),(9,6)}
(iv)

{(6,8),(7,3),(1,3),(7,8),(10,8),(1,4)}
(v)

{(6,8),(7,3),(1,3),(10,8),(1,4)}

Question 15

15.

If A =
{7,1,6,4}
and B =
{2,4,7,1}
,

find the roster form of the relation
R

:

A

→

B
shown in the diagram

(i)

{(4,7),(7,1),(6,1),(1,1)}
(ii)

{(4,7),(7,1),(6,1),(1,1),(8,0)}
(iii)

{}
(iv)

{(4,7),(1,7),(6,1),(1,1)}
(v)

{(4,7),(7,1),(1,7),(6,1),(1,1)}

Question 16

16.

If A =
{g,f,h,m,a}
and B =
{q,k,c,s,i}
,

which of the following is relation
R

:

A

→

B
?

(i)

{(g,i),(a,k),(g,s),(a,q),(a,c)}
(ii)

{(c,d),(i,j),(k,j),(i,b),(q,d)}
(iii)

{(d,a),(j,g),(d,f),(l,m),(d,m)}
(iv)

{(f,b),(f,l),(m,p),(h,p),(a,l)}
(v)

{(s,m),(c,a),(q,g),(q,h),(k,a)}

Question 17

17.

Find the domain from the given graphical representation of relation R.

(i)

{6,7,1,2,8,3}
(ii)

{8,6,7,2}
(iii)

{4,3,5}
(iv)

{8,6,7,2,3}
(v)

{6,7,1,2,8}

Question 18

18.

Find the range from the given graphical representation of relation R.

(i)

{2,8,7,4,3}
(ii)

{2,8,7,4}
(iii)

{6,1,5}
(iv)

{1,6,3,5,7}
(v)

{4,2,8}

Question 19

19.

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)

{b,e,d}
(ii)

{c,a,d}
(iii)

{d,e}
(iv)

{a,d}
(v)

{b,e}

Question 20

20.

If n(A) = 1 and n(B) = 1 then the number of possible relations from A → B is

(i)

0
(ii)

2
(iii)

1
(iv)

4
(v)

(-1)

Question 21

21.

(i)

{(8,3),(6,3),(7,3),(8,5),(6,5),(7,5),(8,1),(6,1),(7,1)}
(ii)

{(8,3),(6,3),(7,3),(8,5),(7,5),(8,1),(6,1),(7,1),(6,5)}
(iii)

{(3,8),(3,6),(3,7),(5,8),(5,6),(5,7),(1,8),(1,6),(1,7)}
(iv)

{}

Question 22

22.

Find the cardinality of the given relation

(i)

5
(ii)

6
(iii)

3
(iv)

4
(v)

2

Question 23

23.

Find the domain and range of the given relation

R

:

A

→

B
=
{(5,1),(5,5),(7,1),(7,5),(9,1),(9,5)}

(i)

A = {2,10,7,9} , B ={5,1,6}
(ii)

A = {7,11,5} , B ={15,1}
(iii)

A = {5,7,9} , B = {1,5}
(iv)

A = {14,9,-3} , B ={5,15}
(v)

A = {9,7,5} , B ={1,7}

Question 24

24.

Write the relation
R

:

A

→

B
in the given diagram,

where A =
{3,7,2,4,10}
and B =
{6,5,8,9}

(i)

{(10,6),(7,9),(10,5),(10,8)}
(ii)

{(10,6),(7,9),(10,9),(10,5),(10,8)}
(iii)

{(10,6),(10,9),(10,5),(10,8),(9,7)}
(iv)

{(10,6),(7,9),(10,9),(10,5),(10,8),(9,7)}
(v)

{}

Question 25

25.

If
f

(

x

)

=

(

3

x

+

9

)
, then find
f

(

7

)

(i)

27
(ii)

30
(iii)

32
(iv)

31
(v)

29

Question 26

26.

(i)

41,25
(ii)

42,26
(iii)

43,27
(iv)

45,29
(v)

44,28

Question 27

27.

find the range

(i)

{-10,29,19,44,12,39}
(ii)

{44,29,39}
(iii)

{32,57,15,19}
(iv)

{29,63,39,19}
(v)

{29,39,44,19}

Question 28

28.

If A =
{q,e,r,m,b}
and B =
{a,n,h,p,l}
,

which of the following is relation
R

:

B

→

A
?

(i)

{(m,n),(b,l),(q,n),(q,p),(e,h)}
(ii)

{(l,o),(h,s),(p,f),(n,o),(h,o)}
(iii)

{(f,q),(f,m),(s,q),(s,m),(o,b)}
(iv)

{(p,q),(n,r),(h,b),(a,m),(l,b)}
(v)

{(e,o),(r,s),(b,f),(q,s),(q,f)}

Question 29

29.

Find the domain of
R

⁻¹
where

R =
{(8,4),(7,2),(10,2),(10,6),(8,2)}

(i)

{4,2,6,9}
(ii)

{10,7,8,3,9,1}
(iii)

{6,2,1}
(iv)

{4,2,6}
(v)

{10,7,3,9,1}

Question 30

30.

Find the domain of
R

⁻¹
from the given diagram.

(i)

{5,8,7,9,10}
(ii)

{9,7,1}
(iii)

{6,2,10,3,4}
(iv)

{6,2,10,3}
(v)

{9,7,1,6}

Question 31

31.

Find the range of
R

⁻¹
where

R =
{(3,7),(10,7),(3,5),(1,2),(4,6)}

(i)

{2,9,5,6,7}
(ii)

{9,5,6,7}
(iii)

{4,10,8,1,2}
(iv)

{3,10,1,4}
(v)

{3,10,1}

Question 32

32.

Find the range of
R

⁻¹
from the given diagram.

(i)

{6,2}
(ii)

{4,9,7,8,3}
(iii)

{6,10,2}
(iv)

{4,9,8,3}
(v)

{6,10,5,9}

Question 33

33.

Find
R

⁻¹
given R =
{(1,3),(8,2),(8,7),(1,2),(8,3)}

(i)

{(3,1),(3,8),(7,8),(2,1),(2,8)}
(ii)

{(3,1),(3,8),(7,8),(2,1),(2,8),(8,3)}
(iii)

{(3,1),(3,8),(2,1),(2,8)}
(iv)

{(3,1),(7,8),(2,1),(2,8),(8,3)}
(v)

{(3,1),(3,8),(2,1),(2,8),(9,6)}

Question 34

34.

(i)

(

(
-13
4
)

,

3

)
(ii)

(

(
-7
2
)

,

1

)
(iii)

(

2

,

(
-7
2
)

)
(iv)

(

(
-7
2
)

,

2

)
(v)

(

(
-5
2
)

,

2

)

Assignment Key