# Tamilnadu state board 10th Maths answers Chapter 1 Relations and Functions Exercise 1.2 - New syllabus

## 10th maths Ex 1.2

- Question 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)}

(ii) R₂ = {(-1, 1)}

(iii) R₃ = {(2, -1), (7, 7), (1, 3)}

(iv) R₄ = {(7,-1), (0, 3), (3, 3), (0, 7)}

(i) A = {1, 2, 3, 7}, B = {3, 0,-1, 7}

(i) R₁ = {(2, 1), (7, 1)}

(ii) R₂ = {(-1, 1)}

(iii) R₃ = {(2, -1), (7, 7), (1, 3)}

(iv) R₄ = {(7,-1), (0, 3), (3, 3), (0, 7)}

(i) A = {1, 2, 3, 7}, B = {3, 0,-1, 7}

*Solution:*

*R₁ = {(2,1), (7,1)}*

It is not a relation there is no element as 1 in B.

(ii) R₂ = {(-1, 1)}

It is not [∵ -1 ∉ A, 1 ∉ B]

(iii) R₃ = {(2, -1), (7, 7), (1, 3)}

It is a relation.

R₄ = {(7,-1), (0, 3), (3, 3), (0, 7)}

It is also not a relation. [∵ 0 ∉ A]It is not a relation there is no element as 1 in B.

(ii) R₂ = {(-1, 1)}

It is not [∵ -1 ∉ A, 1 ∉ B]

(iii) R₃ = {(2, -1), (7, 7), (1, 3)}

It is a relation.

R₄ = {(7,-1), (0, 3), (3, 3), (0, 7)}

It is also not a relation. [∵ 0 ∉ A]

*Question 2.*

*Question 2.*

*Let A = {1, 2, 3, 4, ….., 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R.*

*Answer:*

*A = {1,2, 3, 4 . . . . 45}*

The relation is defined as “is square of’

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}The relation is defined as “is square of’

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}

*Question 3.*

*Question 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.*

Solution:

x = {0, 1, 2, 3, 4, 5}

y = x + 3Solution:

x = {0, 1, 2, 3, 4, 5}

y = x + 3

⇒ y = {3, 4, 5, 6, 7, 8}

*R = {(x, y)}= {(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}*

*Question 4.*

*Question 4.*

*Represent each of the given relation 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)

(ii) {(x, y)|y = x + 3, x, y are natural numbers <10}

(i) {(x, y)|x = 2y,x ∈ {2, 3, 4, 5},y ∈ {1, 2, 3, 4)

(ii) {(x, y)|y = x + 3, x, y are natural numbers <10}

*Solution:*

*(i){(x, y)|x = 2y, x ∈ {2, 3, 4, 5},y ∈ {1, 2, 3, 4}} R = (x = 2y)*

2 = 2 × 1 = 2

4 = 2 × 2 = 42 = 2 × 1 = 2

4 = 2 × 2 = 4

*(c) {(2, 1), (4, 2)}*

*(ii) {(x, y)|y = x + 3, x,+ are natural numbers <10}x = {1, 2, 3, 4, 5, 6, 7, 8, 9} R = (y = x + 3)y = {1, 2, 3, 4, 5, 6, 7, 8, 9}R = {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)}*

*Question 5.*

*Question 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 A, A₂, A₃, A₄ and As 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.

- Solution:

A – Assistants → A₁, A₂, A₃, A4₄, A₅

C – Clerks → C₁, C2₂, C₃, C4₄

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)}