GSEB Solutions Class 11 Maths Chapter 1 Sets Ex 1.3

Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 1 Sets Ex 1.3 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 11 Maths Chapter 1 Sets Ex 1.3

Question 1.
Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:

1. (2, 3, 4,} {1, 2, 3, 4, 5}
2. {a, b, c] {b, c, d)
3. {JC : x is a student of Class XI of your school} ……………….. {x : x is a student of your school}
4. {x : x is a circle in the plane} …………………….. {x : x is a rectangle in the plane}
5. {x : x is a traiangle in the plane} ……………………. {x : x is a rectangle in the plane}
6. {x : x is an equilateral traiangle in the plane} ………………….. {x : x is a traiangle in the plane}
7. {x : x is an even natural number} …………………… {x : x is an integer}.

Solution:

1. ⊂
2. ⊄
3. ⊂
4. ⊄
5. ⊄
6. ⊂
7. ⊄

Question 2.
Examine whether the following statements are true or false:

1. {a, b} ⊄ {b, c, a}
2. [a, e} ⊂ (x : x is a vowel in the English alphabet}
3. {1, 3, 5} ⊂ {1, 3, 5}
4. {a} ⊂ {a, b, c}
5. {a} ∈ {a, b, c}
6. {x : x is an even natural number which divides 6} ⊂ {x : x is a natural number which divides 36}.

Solution:
1. Since the elements of the set {a, b} are also present in the set {b, c, a}, therefore (a, b} ⊄ {b, c, a} is false.

2. Vowels in the English alphabets are a, e, i, o, u.
∴ {α, e) ⊂{x : x is a vowel in the English alphabet} is true.

3. {1, 3, 5} ⊂ {1, 3, 5} is true, as they are equal sets.

4. True as {a} is contained in the set {a, b, c}.

5. False because α ∈ {a, b, c} and not {a}.

6. {x : x is an even natural number less than 6} = {2, 4} and {x : x is a natural number which divides 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36}, since every element of set (2, 4} is contained in the set fl, 2, 3, 4, 6, 9, 12, 18, 36}, therefore the given statement is true.

Question 3.
Let A = {1, 2, {3, 4}, 5}. Which of the following statements are correct and why?

1. {3, 4} ⊂ A
2. {3, 4} ∈ A
3. 1 ∈ A
4. 1 ⊂ A
5. {1, 2, 5} ⊂ A
6. {1, 2, 5) ∈ A
7. {1, 2, 3} ⊂ A
8. ϕ ⊂ A
9. {ϕ} ⊂ A

Solution:

1. Incorrect
2. Correct
3. Correct
4. Incorrect
5. Correct
6. Incorrect
7. Incorrect
8. Incorrect
9. Correct
10. Incorrect

Question 4.
Write down all the subsets of the following subsets;

1. {a}
2. {a, 6}
3. {1, 2, 3}
4. ϕ

Solution:

1. ϕ, {a}
2. ϕ, {a}, {b}, {a, b}
3. ϕ, {1}, {2}, {3}, {1, 2}, (2, 3}, {1, 3}, {1, 2, 3}
4. ϕ

Question 5.
How many elements has P(A), if A = ϕ?
Solution:
If A = ϕ, then by the definition of power set, we have P(A) = P(ϕ) = {ϕ}
= a set containing 1 element.

Question 6.
Write the following as intervals:

1. {x : x ∈ R, -4 < x ≤ 6)
2. {x : x ∈ R, – 12 < x < – 10}
3. {x : x ∈ R, 0 ≤ x < 7}
4. {x : x ∈ R, 3 ≤ x ≤ 4}

Solution:
Given intervals are

1. (-4, 6]
2. (- 12, – 10)
3. [0, 7)
4. [3, 4]

Question 7.
Write the following intervals in the set builder form:

1. (- 3, 0)
2. [6, 12]
3. (6, 12]
4. [- 23, 5)

Solution:

1. (- 3, 0) = {x : x ∈ R, – 3 < x < 0}
2. [6, 12] = {x : x ∈ R, 6 ≤ x ≤ 12}
3. (6, 12] = {x : x ∈ R, 6 < x ≤ 12}
4. [- 23, 5) = {x : x ∈ R, – 23 ≤ x < 5}.

Question 8.
What universal set would you propose for each of the following:
(i) The set of right triangles.
(ii) The set of isosceles triangles.
Solution:
The set of all the possible triangles is the universal set for each of the given sets.

Question 9.
Given the sets A = [1, 3, 5}, B = [2, 4, 6}, C = [0,2, 4, 6, 8}. Which of the following may be considered as universal set(s) for all the three sets A, B and C?
(i) [0,1, 2, 3, 4, 5, 6}
(ii) ϕ
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}
Solution:
The set (iii), i.e., {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the given sets A, B and C.