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

# 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 4 **∈** B.

**Question 4 :**

Represent the following sets in Roster form.

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

**Answer :**

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}

**Answer :**

27 is the value of 3^{3}, 216 is the value of 6^{3}

C = {4^{3}, 5^{3}}

C = {64, 125}

(iv) D = {x : x ∈ Z, –5 < x ≤ 2}

**Answer :**

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.

**Answer :**

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

(ii) C = {1/2, 2/3, 3/4, ..........}

**Answer :**

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.

**Answer :**

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

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

**Answer :**

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}

**Answer :**

P = The set of English months starting with J

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

**Answer :**

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

(iii) R = {x : x ∈ N, x < 5}

**Answer :**

R = The set of natural numbers less than 5.

(iv) S = {x : x is a consonant in English alphabets}

**Answer :**

S = The set of consonants in English alphabets