Pedagogy of Mathematics (Part II) - Set language introduction and ex.1.1, Set Language, Maths, IX std Maths, Samacheerkalvi maths, II year B.Ed., Pedagogy

1. PEDAGOGY OF
MATHEMATICS – PART II
By
Dr. I. Uma Maheswari
Principal
Peniel Rural College of Education,Vemparali, Dindigul District
iuma_maheswari@yahoo.co.in

2. Syllabus
Tamil Nadu Government Samacheer Kalvi
IX and X std Mathematics book

13. STD IX
CHAPTER 1 – SET LANGUAGE
Introduction and Ex - 1.1

21. Solution:
Which are sets
1.Collection of pen
2.Collection of dolls
3.Collection of books
4.Collection of red flower etc.
Which are not sets
1.Collection of good students in a class.
2.Collection of beautiful flowers in a garden etc.

41. Exercise 1.1
Which of the following are sets?
(i) The Collection of prime numbers upto 100.
Solution :
The above statement is well defined, the set will contain 2, 3, 5, 7,
..........97.
Hence it is a set.

42. (ii) The Collection of rich people in India.
Solution :
The set is not well defined. Hence it is not a set.
(iii) The Collection of all rivers in India.
Solution :
The statement is well defined. Hence it is a set.

43. (iv) The Collection of good Hockey players.
Solution :
The statement is not well defined. Hence it is not a set.

44. Question 2 :
List the set of letters of the following words in Roster form.
(i) INDIA (ii) PARALLELOGRAM
(iii) MISSISSIPPI (iv) CZECHOSLOVAKIA
Solution :
Now we have to write the letters of the given word. If we have repeated letters, then we have
to write it once.
(i) INDIA
A = {I, N, D, A}

45. (ii) PARALLELOGRAM
B = {P, A, R, L, E, O, G, M}
(iii) MISSISSIPPI
C = {M, I, S, P}
(iv) CZECHOSLOVAKIA
D = {C, Z, E, H, O, S, L, V, A, K, I}

46. Question 3 :
Consider the following sets A = {0, 3, 5, 8}, B = {2, 4, 6, 10} and
C = {12, 14,18, 20}.
(a) State whether True or False:
(i) 18 ∈ C (ii) 6 ∉ A (iii) 14 ∉ C (iv) 10 ∈ B
(v) 5 ∉ B (vi) 0 ∉ B

47. Solution :
(i) 18 ∈ C
18 is the element of set C, hence it is true.
(ii) 6 ∉ A
The set A does not contain the element 6, hence it is true.
(iii) 14 ∉ C
14 is the element of set C, hence the statement is false.
(iv) 10 ∈ B
10 is the element of set B, hence the statement is true.

48. (b) Fill in the blanks:
(i) 3 ∈ ____ (ii) 14 ∈ _____ (iii) 18 ____ B (iv) 4 _____ B
Solution :
3 is the element of set A, so 3 ∈ A.
14 is the element of set C, so 14 ∈ C.
18 is the element of set C, so 18 ∈ C.
4 is the element of set B, so 4 ∈ B.

49. Question 4 :
Represent the following sets in Roster form.
(i) A = The set of all even natural numbers less than 20.
Solution :
The given set will contain even natural numbers lesser than 20.
A = {2, 4, 6, 8, 10, 12, 14, 16, 18}

50. (ii) B = {y : y = 1/2n , n ∈ N, n ≤ 5}
Solution :
B = {y : y = 1/2n , n ∈ N, n ≤ 5}
If n = 1, then y = 1/2
If n = 2, then y = 1/4
If n = 3, then y = 1/6
If n = 4, then y = 1/8
If n = 5, then y = 1/10 B = { 1/2, 1/4, 1/6, 1/8, 1/10 }

51. (iii) C = {x : x is perfect cube, 27 < x < 216}
Solution :
27 is the value of 33, 216 is the value of 63
C = {43, 53}
C = {64, 125}
(iv) D = {x : x ∈ Z, –5 < x ≤ 2}
Solution :
D = {-4, -3, -2, -1, 0, 1, 2}

52. Question 5 :
Represent the following sets in set builder form.
(i) B = The set of all Cricket players in India who scored double
centuries in One Day Internationals.
Solution :
B = {x : x is an Indian player who scored double centuries in
One Day International}

53. (ii) C = {1/2, 2/3, 3/4, ..........}
Solution :
By observing the given set, the denominator is 1 greater than the numerator.
C = {x : x = n/(n + 1) where n ∈ N}
(iii) D = The set of all Tamil months in a year.
Solution :
D = {x : x is the set of all Tamil months in a year.}

54. (iv) E = The set of odd Whole numbers less than 9.
Solution :
E = {x: x is the set of odd Whole numbers less than 9}

55. Question 6 :
Represent the following sets in descriptive form.
(i) P = { January, June, July}
Solution :
P = The set of English months starting with J
(ii) Q = {7, 11, 13, 17, 19, 23, 29}
Solution :
Q = the set of prime numbers between 5 and 31.

56. (iii) R = {x : x ∈ N, x < 5}
Solution :
R = The set of natural numbers less than 5.
(iv) S = {x : x is a consonant in English alphabets}
Solution :
S = The set of consonants in English alphabets

57. The End