**Samacheer Kalvi 10th Maths Book Back Solution:**

Tamil Nadu **10th Maths Book Back Answers Unit 1 – Relations and Functions Ex 1.2** are provided on this page. Samacheer Kalvi Maths Book Back Solutions/ Guide available for all Units. TN Samacheer Kalvi 10th Maths Book consists of 8 Units and each unit book back solutions given below topics wise with Questions and Answers. The complete** Samacheer Kalvi Books Back Answers/Solutions** are available on our site.

The Samacheer kalvi 10th Maths solutions are useful to enhance your skills. Candidates who prepared for the Competitive and board exams 10th Maths Book Back Answers in English and Tamil Medium. The 10th Maths Unit 1 Relation and Functions consist of 6 units. Each Unit Book Back Answers provide topic-wise on this page. 10th Maths Book Back Answers are prepared according to the latest syllabus. The 10th Maths Book Back Relations and Functions Ex 1.2 Answers in English.

**10th Maths Book Back Answers/Solutions:**

TN Samacheer Kalvi 10th Maths Chapter 1 Book Back Exercise given below. The 10th Maths Book Back Solutions Guide is uploaded below,

**Chapter 1**

**Exercise 1.2 Relations and Functions**

1. Let A = {1, 2, 3, 7} and B = {3, 0, -1, 7}, which of the following are relation from A to B ?

(i) R_{1} = {(2, 1), (7, 1)}

(ii) R_{2} = {(-1, 1)}

(iii) R_{3} = {(2, -1), (7, 7), (1, 3)}

(iv) R_{4} = {(7,-1), (0, 3), (3, 3), (0, 7)}

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

**Solu.:**

R_{1} = {(2,1), (7,1)}

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

(ii) R_{2} = {(-1, 1)}

It is not [∵ -1 ∉ A, 1 ∉ B]

(iii) R_{3} = {(2, -1), (7, 7), (1, 3)}

It is a relation.

R_{4} = {(7,-1), (0, 3), (3, 3), (0, 7)}

It is also not a relation. [∵ 0 ∉ A]

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.

**Solu.:**

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}

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.

**Solu.:
**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}

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}

**Solu.:
**(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 = 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)}

(c) R = {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)}

5. A company has four categories of employees given Assistants (A), Clerks (C), Managers (M), and an Executive Officer (E). The company provides Rs.10,000, Rs.25,000, Rs.50,000, and Rs.1,00,000 as salaries to the people who work in categories A, C, M, and E respectively. If A_{1}, A_{2}, A_{3}, A_{4,} and As were Assistants; C_{1}, C_{2}, C_{3}, C_{4} were Clerks; M_{1}, M_{2}, M_{3} were managers, and E_{1}, E_{2} 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.

**Solu.:
**A – Assistants → A

_{1}, A

_{2}, A

_{3}, A

_{4}, A

_{5}

C – Clerks → C

_{1}, C

_{2}, C

_{3}, C

_{4}

D – Managers → M

_{1}, M

_{2}, M

_{3}

E – Executive officer → E

_{1}, E

_{2}

(a) R = {(10,000, A

_{1}), (10,000, A

_{2}), (10,000, A

_{3}),

(10,000, A

_{4}), (10,000, A

_{5}), (25,000, C

_{1}),

(25,000, C

_{2}), (25,000, C

_{3}), (25,000, C

_{4}),

(50,000, M

_{1}), (50,000, M

_{2}), (50,000, M

_{3}),

(1,00,000, E

_{1}), (1,00,000, E

_{2})}

(b)

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