**Exercise 1.1 Sets**

**Question and Answers**

**Class 11 – Maths**

Class | Class 11 |

Subject | Mathematics |

Chapter Name | Sets |

Chapter No. | Chapter 1 |

Exercise | Exercise 1.1 |

Category | Class 11 Maths NCERT Solutions |

**Question 1 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 the world.**

**Answer **

**(i)** The collection of all months of a year beginning with the letter J is a well-defined collection of objects as one can identify a month which belongs to this collection.

Therefore, this collection is a set.

**(ii)** The collection of ten most talented writers of India is not a well-defined collection as the criteria to determine a 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 as the criteria to determine 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 as you can identify a boy who belongs to this collection.

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 as one can find any book which belongs to this collection.

Therefore, this collection is a set.

**(vii)** The collection of all even integers is a well-defined collection as one can find an integer which belongs to this collection.

Therefore, this collection is a set.

**(viii)** The collection of questions in this chapter is a well-defined collection as one can find a question which belongs to this chapter.

Therefore, this collection is a set.

**(ix) **A collection of most dangerous animals of the world is not a well-defined collection as the criteria to find the dangerousness of an animal can differ from one animal to another.

Therefore, this collection is not 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**

**Answer**

(i) 5 ∈ A

(ii) 8 ∉ A

(iii) 0 ∉ A

(iv) 4 ∈ A

(v) 2 ∈ A

(vi) 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}**

** (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**

**Answer**

**(i)** A = {*x*: *x* is an integer and –3 < *x *< 7}

–2, –1, 0, 1, 2, 3, 4, 5, and 6 only are the elements of this set.

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}

1, 2, 3, 4, and 5 only are the elements of this set

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}

17, 26, 35, 44, 53, 62, 71, and 80 only are the elements of this set

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}

The divisors of 60 are 2,3,4,5,6. Among these, the prime numbers are 2, 3, 5

The elements of the set are 2 , 3 , 5

∴The roaster form of the set D={ x:x is a prime number which is divisor of 60 } is D= { 2 , 3 , 5}

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

TRIGONOMETRY is a 12 letters word out of which T, R and O are repeated.

Hence, the given set can be written in roster form as

E = {T, R, I, G, O, N, M, E, Y}

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

BETTER is a 6 letters word out of which E and T are repeated.

Hence, the given set can be written in roster form as

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}**

**Answer **

**(i) **{3, 6, 9, 12}

The given set can be written in the set-builder form as {*x*:* x* = 3*n*, *n *∈ N and 1 ≤ *n* ≤ 4}

**(ii)** {2, 4, 8, 16, 32}

We know that 2 = 2^{1}, 4 = 2^{2}, 8 = 2^{3}, 16 = 2^{4}, and 32 = 2^{5}.

Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {*x*:* x* = 2* ^{n}*,

*n*∈ N and 1 ≤

*n*≤ 5}.

**(iii)** {5, 25, 125, 625}

We know that 5 = 5^{1}, 25 = 5^{2}, 125 = 5^{3}, and 625 = 5^{4}.

Therefore, the given set {5, 25, 125, 625} can be written in the set-builder form as {*x*:* x* = 5* ^{n}*,

*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 = 1^{2}, 4 = 2^{2}, 9 = 3^{2} …100 = 10^{2}.

Therefore, the given set {1, 4, 9… 100} can be written in the set-builder form as {*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, – 1/ 2 < x < 9/ 2 }**

** (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 }.**

**Answer **

**(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, x^{2} ≤ 4}

We know that

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

Here

0^{2} = 0 ≤ 4, 1^{2} = 1 ≤ 4, 2^{2} = 4 ≤ 4, 3^{2} = 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}

**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} |

**Answer **

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

(ii) {2, 3} | (a) {x : x is a prime number and a divisor of 6} |

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

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

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