# EXERCISE 1.1

**1. Which of the following are sets? Justify our answer.(Ex 1.1 ncert maths solution class 11 )**

**(i) The collection of all months of a year beginning with the letter J.**

**(ii) The collection of the ten most talented writers of India.**

**(iii) A team of eleven best-cricket batsmen of the world.**

**(iv) The collection of all boys in your class.**

**(v) The collection of all natural numbers less than 100.**

**(vi) A collection of novels written by the writer Munshi Prem Chand.**

**(vii) The collection of all even integers.**

**(viii) The collection of questions in this Chapter.**

**(ix) A collection of the most dangerous animals in the world.**

**Solution: (i)** A = { January , Jun , July}

The collection of all months of a year beginning with the letter J is a well-defined collection of objects.

**Therefore, this collection is a set.**

**(ii)** The collection of the ten most talented writers of India is not a well-defined collection, because writer’s talent may differ from one person to another.

**Therefore, this collection is not a set.**

**(iii)** A team of eleven best-cricket batsmen of the world is not a well-defined collection, because a batsman’s talent may vary from one person to another.

**Therefore, this collection is not a set.**

**(iv)** The collection of all boys in your class is a well-defined collection. Because collection of boys are same for every person.

**Therefore, this collection is a set.**

**(v)** The collection of all natural numbers less than 100 is a well-defined collection, as one can find a number which belongs to this collection.

**Therefore, this collection is a set.**

**(vi)** A collection of novels written by the writer Munshi Prem Chand is a well-defined collection

**Therefore, this collection is a set.**

**(vii)** The collection of all even integers is a well-defined collection,

**Therefore, this collection is a set.**

**(viii)** The collection of questions in this Chapter is a well-defined collection,

**Therefore, this collection is a set.**

**(ix)** A collection of the most dangerous animals in the world is not a well-defined collection,the dangerousness of an animal can differ from one animal to another.

**Therefore, this collection is not a set.**

**2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces.**

**(i) 5…A (ii) 8…A (iii) 0…A**

**(iv) 4…A (v) 2…A (vi) 10…A**

**Solution:**

**(i)**

**(ii)**

**(iii)**

**(iv)**

**(v)**

**(vi)**

**3. Write the following sets in roster form.**

**(i) A = { x: x is an integer and –3 < x < 7}.**

**(ii) B = { x: x is a natural number less than 6}.**

**(iii) C = { x: x is a two-digit natural number such that the sum of its digits is 8}**

**(iv) D = { x: x is a prime number which is divisor of 60}.**

**(v) E = The set of all letters in the word TRIGONOMETRY.**

**(vi) F = The set of all letters in the word BETTER.**

**Solution: (i)** A = {*x*: *x* is an integer and –3 < *x *< 7}

Hence, the given set can be written in roster form as

**A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}**

**(ii)** B = {*x*: *x* is a natural number less than 6}

Hence, the given set can be written in roster form as

B = {1, 2, 3, 4, 5}

**(iii) **C = {*x*: *x* is a two-digit natural number such that the sum of its digits is 8}

Hence, the given set can be written in roster form as

C = {17, 26, 35, 44, 53, 62, 71, 80}

**(iv) **D = {*x*: *x* is a prime number which is divisor of 60}

Here, 60 = 2 × 2 × 3 × 5

Hence, the given set can be written in roster form as

D = {2, 3, 5}

**(v)** E = The set of all letters in the word TRIGONOMETRY

Hence, the given set can be written in roaster form as

E = {T, R, I, G, O, N, M, E, Y}

**(vi) **F = The set of all letters in the word BETTER

Hence, the given set can be written in roster form as

F = {B, E, T, R}

**4. Write the following sets in the set-builder form.**

**(i) (3, 6, 9, 12) **

**(ii) {2, 4, 8, 16, 32}**

**(iii) {5, 25, 125, 625} **

**(iv) {2, 4, 6 …}**

**(v) {1, 4, 9 … 100}**

**Solution: (i) **{3, 6, 9, 12}

The given set can be written in the set-builder form as {*x*:* x* = 3*n*, *n *∈ N and 1 ≤ *n* ≤ 4}.

**(ii)** {2, 4, 8, 16, 32}

Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {*x*:* x* = 2* ^{n}*,

*n*∈ N and 1 ≤

*n*≤ 5}.

**(iii)** {5, 25, 125, 625}

We know that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.

Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as {*x*:* x* = 5* ^{n}*,

*n*∈N and 1 ≤

*n*≤ 4}.

**(iv)** {2, 4, 6 …}

{2, 4, 6 …} is a set of all even natural numbers.

Therefore, the given set {2, 4, 6 …} can be written in the set-builder form as {*x*:* x* is an even natural number}.

**(v)** {1, 4, 9 … 100}

We know that 1 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}.

Therefore, the given set {1, 4, 9… 100} can be written in the set-builder form as {*x*:* x* = *n*^{2}, *n *∈ N and 1 ≤ *n* ≤ 10}.

**5. List all the elements of the following sets.**

**(i) A = { x: x is an odd natural number}**

**(ii) B = { x: x is an integer, -1/2 < x < 9/2}**

**(iii) C = { x: x is an integer, x^{2} ≤ 4}**

**(iv) D = { x: x is a letter in the word “LOYAL”}**

**(v) E = { x: x is a month of a year not having 31 days}**

**(vi) F = { x: x is a consonant in the English alphabet which proceeds k}**

**Solution:**

**(i)** A = {*x*: *x* is an odd natural number}

So, the elements are A = {1, 3, 5, 7, 9 …..}.

**(ii)** B = {*x*: *x* is an integer, -1/2 < x < 9/2}

We know that – 1/2 = – 0.5 and 9/2 = 4.5

So, the elements are B = {0, 1, 2, 3, 4}.

**(iii)** C = {*x*: *x* is an integer, x^{2} ≤ 4}

We know that

(–1)^{2} = 1 ≤ 4; (–2)^{2} = 4 ≤ 4; (–3)^{2} = 9 > 4

Here,

0^{2} = 0 ≤ 4, 1^{2} = 1 ≤ 4, 2^{2} = 4 ≤ 4, 3^{2} = 9 > 4

So, we get

C = {–2, –1, 0, 1, 2}

**(iv)** D = {*x*: *x* is a letter in the word “LOYAL”}

So, the elements are D = {L, O, Y, A}

**(v)** E = {*x*: *x* is a month of a year not having 31 days}

So, the elements are E = {February, April, June, September, November}

**(vi)** F = {*x*: *x* is a consonant in the English alphabet which proceeds *k*}

So, the elements are F = {b, c, d, f, g, h, j}

**6. Match each of the sets on the left in the roster form with the same set on the right described in the set-builder form.**

**(i) {1, 2, 3, 6} (a) {x: x is a prime number and a divisor of 6}**

**(ii) {2, 3} (b) {x: x is an odd natural number less than 10}**

**(iii) {M, A, T, H, E, I, C, S} (c) {x: x is a natural number and divisor of 6}**

**(iv) {1, 3, 5, 7, 9} (d) {x: x is a letter of the word MATHEMATICS}**

**Solution:**

**(i)** Here, the elements of this set are natural numbers as well as divisors of 6.

Hence, **(i) → (c).**

**(ii)** 2 and 3 are prime numbers which are divisors of 6.

Hence,** (ii) → (a).**

**(iii)** The elements are the letters of the word MATHEMATICS.

Hence, **(iii) → (d).**

**(iv)** The elements are odd natural numbers which are less than 10.

Hence, **(v)→ (b).**