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# Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 1 Set Language Ex 1.1

Question 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.

(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.

(iv) The Collection of good Hockey players.

Solution :

The statement is not well defined. Hence it is not a set.

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}

(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}

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

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.

(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   B.

Question 4 :

Represent the following sets in Roster form.

(i) A = The set of all even natural numbers less than 20.

The given set will contain even natural numbers lesser than 20.

A  =  {2, 4, 6, 8, 10, 12, 14, 16, 18}

(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 }

(iii) C = {x : x is perfect cube, 27 < x < 216}

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}

D  =  {-4, -3, -2, -1, 0, 1, 2}

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.

B = {x : x is an Indian player who scored double centuries in One Day International}

(ii)  C = {1/2, 2/3, 3/4, ..........}

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.

D = {x : x is the set of all tamil months in a year.}

(iv) E = The set of odd Whole numbers less than 9.

E = {x: x is the set of odd Whole numbers less than 9}

Question 6 :

Represent the following sets in descriptive form.

(i) P = { January, June, July}

P = The set of English months starting with J

(ii) Q = {7, 11, 13, 17, 19, 23, 29}

Q =  the set of prime numbers between 5 and 31.

(iii) R = {x : x  ∈  N, x < 5}