Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 1 Sets Ex 1.1 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 1 Sets Ex 1.1

Question 1.
Which of the following are sets? Justify your answer?

1. The collection of all months of a year beginning with letter J.
2. The collection of ten most talented writers of India, (iit) A team of eleven best cricket batsmen of the world.
3. The collection of all boys in your class.
4. The collection of all natural numbers less than 100.
5. The collection of all natural numbers less than 100.
6. A collection of novels written by the writer Munshi Prem Chand.
7. The collection of all even integers.
8. The collection of questions in this chapter.
9. A collection of most dangerous animals of the world.

Solution:
1. We can definitely say that the members of this collection are:
January, June, July.
So, this collection is well-defined and hence, it is a set.

2. The term ‘most talented’ is a vague term. A writer may be most talented to one person and may not be so to the other.
Thus, we cannot judge definitely which writers are there in our collection.
∴ This collection is not well-defined and hence, it is not a set.

3. The term ‘best’ is a vague term. A batsmen may be best to one person and may not be so to the other.
Thus, we cannot judge definitely which batsmen are there in our collection.
∴ This collection is not well-defined and hence, it is not a set.

4. We will definitely say that the members of this collection are your classfellows.
∴ This collection is well-defined and hence, it is a set.

5. Clearly, the members of collection are 1,2, 3, …, 97, 98, 99.
∴ This collection is well-defined and hence, it is a set.

6. Clearly, the members of collection are the novels written by Munshi Prem Chand.
∴ This collection is well-defined and hence, it is a set.

7. We can definitely say that the members of this collection are 2, 4, 6,
∴ This collection is well-defined and hence, it is a set.

8. Clearly, the members of the collection are the different questions of this chapter.
So, it is well-defined and hence, it is a set.

9. The term ‘most dangerous’ is a vague term. An animal may be most dangerous to one person and may not be so to the other. So, it is not a set.

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

1. 5 …………………. A
2. 8 …………………….. A
3. 0 ………………………. A
4. 4 …………………….. A
5. 2 ………………………… A
6. 10 ……………………………. A

Solution:

1. 5 ∈ A
2. 8 ∉ A
3. 4 ∉ A
4. 4 ∈ A
5. 2 ∈ A
6. 10 ∉ A

Question 3.
Write the following sets in the roster form:

1. A = [x : x is an integer and – 3 ≤ x < 7}
2. B = {x : x is a natural number less than 6}
3. G = {x : x is a two digit natural number such that sum of its digits is 8}
4. D = {x : x is a prime number which is a divisor of 60}
5. E = the set of all letters in the word TRIGONOMETRY.
6. F = the set of all letters in the word BETTER.

Solution:

1. A = {- 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6}
2. B = {1, 2, 3, 4, 5}
3. C = {17, 26, 36, 44, 63, 62, 71, 80}
4. D = {2, 3, 5}
5. E = {T, R, I, G, O, N, M, E, Y}
6. F = {B, E, T, R}

Question 4.
Write the following sets in the set builder form:

1. {3, 6, 9, 12}
2. {2, 4, 8, 16, 32}
3. {5, 25, 125, 625}
4. {2, 4, 6, …}
5. {1, 4, 9, … , 100}

Solution:

1. A = [x : x is a natural number multiple of 3 and x < 15}
2. B = {x : x = 2ⁿ, n ∈ N and n ≤ 6}
3. C = {x : x = 5ⁿ, and n ∈ N and n ≤ 4}
4. D = {2 : x is an even natural number}
5. E = {x : x = n², n ∈ N and n < 11}

Question 5.
List all the elements of the following sets:

1. A = {x : x is an odd natural number}
2. B = {x : x is an integer, – (frac{1}{2}) < x < (frac{9}{2})}
3. C = {x : x is an integer, x² ≤ 4}
4. D = (x : x is a letter in the word “LOYAL”}
5. E = {x : x is a month of a year not having 31 days}
6. F = {x : x is a consonant in the English alphabet which precedes k).

Solution:

1. A = (1, 3, 5, 7, …}
2. B = {0, 1, 2, 3, 4}
3. C = {- 2, – 1, 0, 1, 2}
4. D = {L, O, Y, A}
5. E = {February, April, June, September, November}
6. F = [b, c, d, f, g, h, j}.

Question 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) ⟷ (c)
(ii) ⟷ (a)
(iii) ⟷ (d)
(iv) ⟷ (b)