TN samacheer kalvi 10th Maths:
Chapter 1 Relations and Functions – Exercise 1.2 solutions
1. Let
A = {1, 2, 3, 7} and B = {3, 0,–1, 7}, which of the
following are relation from A to
B?
(i)
R1
= {(2,1), (7,1)} – It is not a relation, because there is no element as ‘1’ in
‘B ’,
1 ∉B (∉-Not belongs to)
(ii)
(ii)
R2= {(–1,1)} – It is not a relation, -1 ∉A & 1 ∉B
(iii)
R3
= {(2,–1), (7,7), (1,3)} – It is a relation
(iv)
R4=
{(7,–1), (0,3), (3,3), (0,7)} – It is not a relation, 0∉A
2. Let
A= {1, 2, 3, 4,..., 45} and R be the relation defined as ”is
square of a number” on A. Write
R as a subset of A´A. Also, find the domain and range of
R.
R={(x,y)}, where x={1,2,3,…..45}
and y=x2
|
|
x=1 |
x=2 |
x=3 |
x=4 |
x=5 |
x=6 |
|
y=x2 |
=12 =1 |
=22 =4 |
=32 =9 |
=42 =16 |
=52 =25 |
=62 =36 |
|
R={(x,y)} |
(1,1) |
(2,4) |
(3,9) |
(4,16) |
(5,25) |
(6,36) |
R = {(1, 1), (2, 4), (3, 9), (4, 16), (5, 25),
(6, 36)}
Domain of R = {1, 2, 3, 4, 5, 6}
Range of R
= {1, 4, 9, 16, 25, 36}
3. A
Relation R is given by the set {(x,y) /y=x + 3, x ∈
{0,1,2, 3, 4,5}}. Determine its domain and range.
R=
{(x,y)}, where x={0,1,2,3,4,5} and y=x+3
|
|
x=0 |
x=1 |
x=2 |
x=3 |
x=4 |
x=5 |
|
y=0+3 |
=0+3 =3 |
=1+3 =4 |
=2+3 =5 |
=3+3 =6 |
=4+3 =7 |
=5+3 =8 |
|
R= {(x,y)} |
(0,3) |
(1,4) |
(2,5) |
(3,6) |
(4.7) |
(5,8) |
R= {(0,3), (1,4), (2,5), (3,6), (4.7), (5,8)
}
Domain
of R = {0, 1, 2, 3, 4, 5}
Range
of R = {3, 4, 5, 6, 7, 8}
4. Represent
each of the given relations by (a) an arrow diagram, (b) a graph and (c) a set
in roster form, wherever possible,
i. {(x,y)|x = 2y, x∈{2,3,4,5}, y ∈{1,2,3,4}
R={(x,y)},
where y={1,2,3,4}, x=2y
|
|
y=1 |
y=2 |
y=3 |
y=4 |
|
x=2y |
=2x1 =2 |
=2x2 =4 |
=2x3 =6 |
=2x4 =8 |
|
R={(x,y)} |
(2,1) |
(4,2) |
(6,3) |
(8,4) |
R= {(2,1),(4,2)}
a)
An
arrow diagram:
b) Graph form:
c)
Roaster form:
R={(2,1),(4,2)}
ii. {(x,y)|y = x+3, x, y are natural
numbers < 10}
R={(x,y)},
where x={1,2,3,4,5,6,7,8,9} and y=x+3(<10)
|
|
x=1 |
x=2 |
x=3 |
x=4 |
x=5 |
x=6 |
|
y=x+3 |
=1+3 4 |
=2+3 5 |
=3+3 =6 |
=4+3 =7 |
=5+3 =8 |
=6+3 =9 |
|
R={(x,y)} |
(1,4) |
(2,5) |
(3,8) |
(4,7) |
(5,8) |
(6,9) |
R =
{(1,4), (2,5), (3,8), (4,7), (5,8), (6,9)}
a)
An
arrow diagram:
b)
Graph
form:
c)
Roaster form:
R={(1,4),
(2,5), (3,8), (4,7), (5,8), (6,9)}
5. A
company has four categories of employees given by Assistants (A), Clerks (C), Managers (M)
and an Executive Officer (E).
The company provide ₹10,000, ₹25,000, ₹50,000 and ₹1,00,000 as salaries to the
people who work in the categories A, C,
M
and E respectively. If A1,
A2,
A3,
A4
and A5 were Assistants; C1,
C2,
C3,C4
were Clerks; M1, M2, M3
were managers and E1, E2 were Executive officers
and if the relation R is defined by xRy,
where x is the salary given to person y,express
the relation R through an ordered pair and an arrow diagram.
A – Assistants → A1,
A2, A3, A4, A5
C – Clerks → C1, C2, C3,
C4
D – Managers → M1, M2, M3
E – Executive officer → E1, E2
a)
R = {(10,000, A1), (10,000, A2),
(10,000, A3), (10,000, A4), (10,000, A5),
(25,000, C1), (25,000,
C2), (25,000, C3), (25,000, C4),
(50,000, M1), (50,000,
M2), (50,000, M3),
(1,00,000, E1),
(1,00,000, E2)}
b)
Arrow diagram:
