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 = 3n, 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 = 2ⁿ, n ∈ N and 1 ≤ n ≤ 5}.

(iii) {5, 25, 125, 625}

We know that 5 = 5¹, 25 = 5², 125 = 5³, and 625 = 5⁴.

Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as {x: x = 5ⁿ, 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 = 1², 4 = 2², 9 = 3² …100 = 10².

Therefore, the given set {1, 4, 9… 100} can be written in the set-builder form as {x: x = n², 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, x² ≤ 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, x² ≤ 4}

We know that

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

Here,

0² = 0 ≤ 4, 1² = 1 ≤ 4, 2² = 4 ≤ 4, 3² = 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).

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