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NCERT Mathematics Class 11 Solutions for all questions in Chapter 1 Exercise 1.3 are given below in PDF format for free download. The solutions are given on the basis of solved examples and unsolved problems. All these solutions contain detailed solution steps, diagrams and graphical representation of the examples/problems.
| Board | SCERT, Kerala |
| Text Book | NCERT Based |
| Class | Plus One |
| Subject | Math's Textbook Solution |
| Chapter | Chapter 1 |
| Exercise | Ex 1.3 |
| Chapter Name | Sets |
| Category | Plus One Kerala |
Kerala Syllabus Plus One Math's Textbook Solution Chapter 1 Sets Exercises 1.3
Chapter 1 Sets Textbook Solution
- Exercises 1.1
- Exercises 1.2
- Exercises 1.3
- Exercises 1.4
- Exercises 1.5
- Exercises 1.6
- Miscellaneous Exercise Chapter 1
Chapter 1 Sets Exercise 1.3
How many elements have P(A), if A = Φ?
We know that if A is a set with m elements i.e., n(A) = m, then n[P(A)] = 2m.
If A = Φ, then n(A) = 0.
∴ n[P(A)] = 20 = 1
Hence, P(A) has one element.
What universal set (s) would you propose for each of the following:
(i) The set of right triangles
(ii) The set of isosceles triangles
(i) Collection of the right triangle is a subset of a set of triangles. The comprehensive set can be a set of triangles or set of polygons
(ii)set of an isosceles triangle is a subset of the game of triangles. the universal set can be a set of triangles or a set of polygons
Write the following as intervals:
(i) {x: x ∈ R, –4 < x ≤ 6}
(ii) {x: x ∈ R, –12 < x < –10}
(iii) {x: x ∈ R, 0 ≤ x < 7}
(iv) {x: x ∈ R, 3 ≤ x ≤ 4}
(i) {x: x ∈ R, –4 < x ≤ 6} = (–4, 6]
(ii) {x: x ∈ R, –12 < x < –10} = (–12, –10)
(iii) {x: x ∈ R, 0 ≤ x < 7} = [0, 7)
(iv) {x: x ∈ R, 3 ≤ x ≤ 4} = [3, 4]
Write the following intervals in set-builder form:
(i) (–3, 0)
(ii) [6, 12]
(iii) (6, 12]
(iv) [–23, 5)
(i) {x:x ∈ R,-3 <x <0}
(ii) {x: x ∈ R ,6 ≤ x ≤ 12}
(iii) {x: x ∈ R, 6 < x ≤ 12}
(iv) {x: x ∈ R,-23 ≤ x < 5}
Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces:
(i) {2, 3, 4} … {1, 2, 3, 4, 5}
(ii) {a, b, c} … {b, c, d}
(iii) {x: x is a student of Class XI of your school} … {x: x student of your school}
(iv) {x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}
(v) {x: x is a triangle in a plane}…{x: x is a rectangle in the plane}
(vi) {x: x is an equilateral triangle in a plane}… {x: x is a triangle in the same plane}
(vii) {x: x is an even natural number} … {x: x is an integer}
(i) 
(ii) 
(iii) {x: x is a student of class XI of your school}⊂ {x: x is a student of your school}
(iv) {x: x is a circle in the plane} ⊄ {x: x is a circle in the same plane with radius 1 unit}
(v) {x: x is a triangle in a plane} ⊄ {x: x is a rectangle in the plane}
(vi) {x: x is an equilateral triangle in a plane}⊂ {x: x in a triangle in the same plane}
(vii) {x: x is an even natural number} ⊂ {x: x is an integer}
Examine whether the following statements are true or false:
(i) {a, b} ⊄ {b, c, a}
(ii) {a, e} ⊂ {x: x is a vowel in the English alphabet}
(iii) {1, 2, 3} ⊂{1, 3, 5}
(iv) {a} ⊂ {a. b, c}
(v) {a} ∈ (a, b, c)
(vi) {x: x is an even natural number less than 6} ⊂ {x: x is a natural number which divides 36}
(i) False. Each element of {a, b} is also an element of {b, c, a}.
(ii) True. a, e are two vowels of the English alphabet.
(iii) False. 2∈{1, 2, 3}; however, 2∉{1, 3, 5}
(iv) True. Each element of {a} is also an element of {a, b, c}.
(v) False. The elements of {a, b, c} are a, b, c. Therefore, {a}⊂{a, b, c}
(vi) True. {x:x is an even natural number less than 6} = {2, 4}
{x:x is a natural number which divides 36}= {1, 2, 3, 4, 6, 9, 12, 18, 36}
Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and why?
(i) {3, 4}⊂ A
(ii) {3, 4}}∈ A
(iii) {{3, 4}}⊂ A
(iv) 1∈ A
(v) 1⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) Φ ∈ A
(x) Φ ⊂ A
(xi) {Φ} ⊂ A
A = {1, 2, {3, 4}, 5}
(i) The statement {3, 4} ⊂ A is incorrect because 3 ∈ {3, 4}; however, 3∉A.
(ii) The statement {3, 4} ∈A is correct because {3, 4} is an element of A.
(iii) The statement {{3, 4}} ⊂ A is correct because {3, 4} ∈ {{3, 4}} and {3, 4} ∈ A.
(iv) The statement 1∈A is correct because 1 is an element of A.
(v) The statement 1⊂ A is incorrect because an element of a set can never be a subset of itself.
(vi) The statement {1, 2, 5} ⊂ A is correct because each element of {1, 2, 5} is also an element of A.
(vii) The statement {1, 2, 5} ∈ A is incorrect because {1, 2, 5} is not an element of A.
(viii) The statement {1, 2, 3} ⊂ A is incorrect because 3 ∈ {1, 2, 3}; however, 3 ∉ A.
(ix) The statement Φ ∈ A is incorrect because Φ is not an element of A.
(x) The statement Φ ⊂ A is correct because Φ is a subset of every set.
(xi) The statement {Φ} ⊂ A is incorrect because of Φ∈ {Φ}; however, Φ ∈ A.
Write down all the subsets of the following sets:
(i) {a}
(ii) {a, b}
(iii) {1, 2, 3}
(iv) Φ
(i) The subsets of {a} are Φ and {a}.
(ii) The subsets of {a, b} areΦ, {a}, {b}, and {a, b}.
(iii) The subsets of {1, 2, 3} areΦ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and
{1, 2, 3}
(iv) The only subset of Φ isΦ.
Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universals 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}
(i) It can be seen that A ⊂ {0, 1, 2, 3, 4, 5, 6}
B ⊂ {0, 1, 2, 3, 4, 5, 6}
However, C ⊄ {0, 1, 2, 3, 4, 5, 6}
Therefore, the set {0, 1, 2, 3, 4, 5, 6} cannot be the universal set for the sets A, B, and C.
(ii) A ⊄ Φ, B ⊄ Φ, C ⊄ Φ
Therefore, Φ cannot be the universal set for sets A, B, and C.
(iii) A ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
C ⊂ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Therefore, the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set for the sets A, B, and C.
(iv) A ⊂ {1, 2, 3, 4, 5, 6, 7, 8}
B ⊂ {1, 2, 3, 4, 5, 6, 7, 8}
However, C ⊄ {1, 2, 3, 4, 5, 6, 7, 8}
Therefore, the set {1, 2, 3, 4, 5, 6, 7, 8} cannot be the universal set for the sets A, B, and C.
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Chapter 1: Sets EX 1.3 Solution
Chapter 1: Sets EX 1.3 Solution- Preview
Plus One Math's Chapter Wise Textbook Solution PDF Download
- Chapter 1: Sets
- Chapter 2: Relations and Functions
- Chapter 3: Trigonometric Functions
- Chapter 4: Principle of Mathematical Induction
- Chapter 5: Complex Numbers and Quadratic Equations
- Chapter 6: Linear Inequalities
- Chapter 7: Permutation and Combinations
- Chapter 8: Binomial Theorem
- Chapter 9: Sequences and Series
- Chapter 10: Straight Lines
- Chapter 11: Conic Sections
- Chapter 12: Introduction to Three Dimensional Geometry
- Chapter 13: Limits and Derivatives
- Chapter 14: Mathematical Reasoning
- Chapter 15: Statistics
- Chapter 16: Probability
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