NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1 is part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1.

- Sets Class 11 Ex 1.2
- Sets Class 11 Ex 1.3
- Sets Class 11 Ex 1.4
- Sets Class 11 Ex 1.5
- Sets Class 11 Ex 1.6
- Sets Class 11 Miscellaneous Exercise

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Sets |

Exercise |
Ex 1.1 |

Number of Questions Solved |
6 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.1

**Question .**

**Which of the following are sets? Justify your answer.**

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

**(ii)** The collection of 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 most dangerous animals of world.

**Solution.
**

**(i)**The collection of all months of a year beginning with J is {J anuary, June, July}, which is well defined and hence it forms a set.

**(ii)**The collection of most talented writers of India is not well defined because opinions about ‘most talented writers’ vary from person to person and hence it does not form a set.

**(iii)**A team of eleven best-cricket batsmen of the world is not well defined because opinions about ‘best-cricket batsmen’ vary from person to person and hence it does not form a set.

**(iv)**The collection of all boys in your class is well defined and hence it forms a set.

**(v)**The collection of all natural numbers less than 100 is {1, 2, 3, 4,…………, 99}, which is well

defined and hence it forms a set.

**(vi)**A collection of novels written by the writer Munshi Prem Chand is well defined and hence it forms a set.

**(vii)**The collection of all even integers is {…………..,-4, -2, 0, 2, 4,……….. } which is well defined and hence it forms a set.

**(viii)**The collection of questions in this chapter is well defined and hence it forms a set.

**(ix)**A collection of most dangerous animals of the world is not well defined because opinions about ‘most dangerous animals’ vary from person to person and hence it does not form a set.

**Question 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)**Since 5 is the element of A. ∴ 5 ∉ A.

**(ii)**As 8 is not the element of A. ∴ 8 ∉ A

**(iii)**As 0 is not the element of A ∴ 0 ∈ A.

**(iv)**4 is the element of A ∴ 4 ∈ A.

**(v)**2 is the element of A ∴ 2 ∈ A.

**(vi)**10 is not the element of A ∴ 10 ∉ A.

**Question 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}

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

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

**Solution.**

**(i)** Integers lying between -3 and 7 are -2, -1, 0, 1, 2, ……….. , 6

∴ A = {-2,-1, 6}.

**(ii)** Natural numbers less than 6 are 1, 2, 3, 4, 5.

∴ B = 11, 2, 3, 4, 5}

**(iii)** Two digit natural numbers such that the sum of its digits is 8 are 17, 26, 35, 44, 53, 62, 71, 80.

∴ C= (17, 26, 35, 44, 53, 62, 71,80}

**(iv)** Prime number divisors of 60 are 2, 3, 5.

∴ D = (2, 3, 5}

**(v)** Word TRIGONOMETRY is formed by using the letters T, R, I, G, O, N, M, E, Y.

∴ E = (T, R, I, G, N, O, M, E, Y}

**(vi)** Word BETTER is formed by using the letters B, E, T, R

∴ F = (B, E, T, R}

**Question 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)** Let A = (3, 6, 9, 12}

All elements of the set are natural numbers that are multiples of 3.

∴ A = (x : x = 3n, n∈N and 1 ≤ n ≤4}

**(ii)** Let B = (2, 4, 8, 16, 32} = (2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}}

∴ B = {x : x = 2^{n}, n ∈ N and 1 ≤ n ≤ 5}

**(iii)** Let C = (5, 25, 125, 625} = (5^{1}, 5^{2}, 5^{3}, 5^{4}}

∴ C = {x : x = 5^{n}, n ∈ N and 1 ≤ n ≤ 4}

**(iv)** Let D = (2, 4, 6,……………..}

All elements of the set are even natural numbers.

∴ D = (x: x is an even natural number)

**(v)** Let E = {1,4,9,……….,100}

All elements of the set are perfect squares.

∴ E = {x: x = n^{2}, n ∈ N and 1 ≤ n ≤ 10}

**Question 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, < x < }

**(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 precedes k}.

**Solution.**

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

∴ A = {1, 3, 5, 7,……………}

**(ii)** B = {x: x is an integer, < x < }

∴ B = { 0, 1, 2, 3, 4}

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

x^{2} ≤ 4⇒ -2 ≤ x ≤ 2

∴ C = {-2, -1, 0, 1, 2}

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

∴ D = {L, O, Y, A}

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

∴ E = {February, April, June, September, November}

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

∴ F = {b, c, d, f, g, h, j}

**Question 6.**

**Match each of the set on the left in the roster form with the same set on the right described in 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 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).

**The sets which are in set-builder form can be written in roster form as follows:
(a)** {x : x is a prime number and a divisor of 6} = {2, 3}

**(b)**{x: x is an odd natural number less than 10} = {1, 3, 5, 7, 9}

**(c)**{x : x is natural number and divisor of 6} = {1, 2, 3, 6}

**(d)**{x: x is a letter of the word MATHEMATICS} = {M, A, T, H, E, I, C, S}

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