10th maths exercise 1-2 solution Guide

 

10th Maths Guide English Medium 

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10th maths Guide English Medium 

10th maths Exercise 1.2 Solution (Answers)

 10th maths Example1.2 Solution // Relation and functions

10th maths "Example 1.4" solution

Question : Let A = {3, 4, 7, 8} and B = {1, 7, 10}. Which of the following sets are relations from A to B ?

(i)  R1 = {(3, 7), (4, 7), (7, 10), (8, 1)} 

(ii)  R2 = {(3, 1), (4, 12)}

(iii)  R3 = {(3, 7), (4, 10), (7, 7), (7, 8), (8, 11),  (8, 7), (8, 10)}

Solution :

A×B = {(3, 1), (3, 7), (3, 10), (4, 1), (4, 7), 

        (4,10), (7,1), (7,7), (7,10), (8, 1), (8, 7), (8, 10)}

(i) We note that R1 ⊆ A × B. Thus, R1 is a relation from A to B. 

(ii) Here, (4, 12) ∈ R2, but (4, 12) ∉ A × B. So, R2 is not a relation from A to B.

 (iii) Here, (7, 8) ∈ R3, but (7, 8) ∉ A × B. So R3 is not a relation from A to B.

10th maths "Example 1.5"solution /Relation and function

Question : The arrow diagram shows a relationship be-tween the sets P and Q. Write the relation in 

(i) Set builder form 

(ii) Roster form 

(iii) What is the domain and range of R.

Solution : 

(i)  Set builder form of  R  = {(x, y) | y = x – 2, x ∈ P, y ∈ Q}

(ii)  Roster form R  = {(5, 3), (6, 4), (7, 5)}

(iii)  Domain of R  = {5, 6, 7} and range of  R = {3, 4, 5}

10th maths EXERCIsE 1.2 solution question number 1 / relation 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) 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)}

Solution : 

Given A = {1, 2, 3, 7}, B = {3, 0, –1, 7}

∴ A × B = {(1, 3), (1, 0), (1, –1), (1, 7),     

                   (2, 3), (2, 0), (2, –1), (2, 7),      

                   (3, 3), (3, 0), (3, –1), (3, 7),      

                   (7, 3), (7, 0), (7, –1), (7, 7)}

i) R1 = {(2, 1), (7, 1)} 

           (2, 1) ∈ R1 but (2, 1) ∉ A × B 

∴ R1 is not a relation from A to B.

ii)  R2 = {(–1, 1)} 

        (–1, 1) ∈ R2 but (–1, 1) ∉ A × B 

∴ R2 is not a relation from A to B.

iii) R3 = {(2, –1), (7, 7), (1, 3)} 

We note that R3 ⊆ A × B 

∴ R3 is a relation.

iv) R4 = {(7, –1), (0, 3), (3, 3), (0, 7)} (0, 3), (0, 7) ∈ R4 but not in A × B. 

∴ R4 is not a relation.

10th maths EXERCIsE 1.2 solution question number 2 / relation and functions

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.

Solution : 

Given A = {1, 2, 3, 4, ........ 45} 

R : “is square of” 

R = {1, 4, 9, 16, 25, 36} 

Clearly R is a subset of A. 

∴ Domain = {1, 2, 3, 4, 5, 6} 

∴ Range = {1, 4, 9, 16, 25, 36}

10th maths EXERCIsE 1.2 solution question number 3 / relation and functions

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 :

 Given R = {(x, y) /  y = x  + 3, 

x  ∈  {0, 1, 2, 3, 4, 5}} 

x =  0  ⇒  y  = 3 x =  1  ⇒  y  = 4 

x =  2  ⇒  y  = 5 x =  3  ⇒  y  = 6 

x =  4  ⇒  y  = 7 x =  5  ⇒  y  = 8 

∴ R = {(0, 3), (1, 4), (2, 5), (3, 6), (4, 7), (5, 8)}

 ∴ Domain : {0, 1, 2, 3,4, 5}    

  Range : {3, 4, 5, 6, 7, 8}

10th maths EXERCIsE 1.2 solution question number 4 / relation and functions

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} 

(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} a)  

Arrow diagram :

b) Graph :

c) a set in roster  : z {(2, 1), (4, 2)} 

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

a)  Arrow Diagram :

b) Graph :

c) a set in roster  : 

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

10th maths EXERCIsE 1.2 solution question number 1 / relation and functions

5. A  company  has  four  categories  of  employees  given  by  Assistants  (A),  Clerks (C),  Managers  (M)  and  an  Executive  Off icer  (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. 

Solution : 

a) Ordered Pair  : 

{(10000,  A₁), (10000,  A₂), (10000,  A₃), (10000,  A₄), (10000,  A₅), (25000, C₁), 

(25000, C₂), (25000, C₃), (25000, C₄), 

(50000, M₁), (50000, M₂), (50000, M₃),   

   (100000, E₁), (100000, E₂s). 

b)  Arrow Diagram :

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