11th SETS

                                                SETS

                                                                             Exercise 1.1

     Page 4 

Q1:- Which of the following are sets? Justify our answer.

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

Ans:-  (i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects because one can definitely identify a month that belongs to this collection.

Hence, this collection is a set.

(ii) The collection of ten most talented writers of India.

ANS:- (ii) The collection of ten most talented writers of India is not a well-defined collection because the criteria for determining a writer’s talent may vary from person to person.

Hence, this collection is not a set.

(iii) A team of eleven best-cricket batsmen of the world.

ANS:- (iii) A team of eleven best cricket batsmen of the world is not a well-defined collection because the criteria for determining a batsman’s talent may vary from person to person.

Hence, this collection is not a set.

(iv) The collection of all boys in your class.

ANS:- (iv) The collection of all boys in your class is a well-defined collection because you can definitely identify a boy who belongs to this collection.

Hence, this collection is a set.

(v) The collection of all natural numbers less than 100.

ANS:- (v) The collection of all natural numbers less than 100 is a well-defined collection because one can definitely identify a number that belongs to this collection.

Hence, this collection is a set.

(vi) A collection of novels written by the writer Munshi Prem Chand.

ANS:- (vi) A collection of novels written by the writer Munshi Prem Chand is a well-defined collection because one can definitely identify a book that belongs to this collection.

Hence, this collection is a set.

(vii) The collection of all even integers.

ANS:- (vii) The collection of all even integers is a well-defined collection because one can definitely identify an even integer that belongs to this collection.

Hence, this collection is a set.

(viii) The collection of questions in this Chapter.

ANS:- (viii) The collection of questions in this chapter is a well-defined collection because one can definitely identify a question that belongs to this chapter.

Hence, this collection is a set.

(ix) A collection of most dangerous animals of the world.

ANS:- (ix) The collection of most dangerous animals of the world is not a well-defined collection because the criteria for determining the dangerousness of an animal can vary from person to person.

Hence, this collection is not a set.

     Page 5

Q2:-Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈or ∉ in the blank spaces:

(i) 5…A

Ans:- (i) 5 ∈ A

(ii) 8…A

Ans:- (ii) 8 ∉ A

(iii) 0…A

Ans:- (iii) 0 ∉ A 

(iv) 4…A

Ans:- (iv) 4 ∈ A

(v) 2…A

Ans:-(v) 2 ∈ A

(vi) 10…A

Ans:-(vi) 10 ∉ A


Q3:-Write the following sets in roster form:

(i) A = {xx is an integer and –3 < < 7}.

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

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

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

A = {–2, –1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {xx is a natural number less than 6}.

Ans:- (ii) B = {x: x is a natural number less than 6}

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

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

B = {1, 2, 3, 4, 5}

(iii) C = {xx is a two-digit natural number such that the sum of its digits is 8}

Ans:-  (iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

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

Therefore, this set can be written in roster form as

C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv) D = {xx is a prime number which is divisor of 60}.

Ans:- (iv) D = {x: x is a prime number which is a divisor of 60}

2

60

2

30

3

15

 

5

∴60 = 2 × 2 × 3 × 5

The elements of this set are 2, 3, and 5 only.

Therefore, this set can be written in roster form as D = {2, 3, 5}.

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

Ans:- (v) E = The set of all letters in the word TRIGONOMETRY

There are 12 letters in the word TRIGONOMETRY, out of which letters T, R, and O are repeated.

Therefore, this 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.

Ans:- (vi) F = The set of all letters in the word BETTER

There are 6 letters in the word BETTER, out of which letters E and T are repeated.

Therefore, this set can be written in roster form as

F = {B, E, T, R}

Q4:-Write the following sets in the set-builder form:

(i) (3, 6, 9, 12)

Ans:-  (i) {3, 6, 9, 12} = {x: x = 3nn∈ N and 1 ≤ n ≤ 4}

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

Ans:- (ii) {2, 4, 8, 16, 32}

It can be seen that 2 = 21, 4 = 22, 8 = 23, 16 = 24, and 32 = 25.

∴ {2, 4, 8, 16, 32} = {x: x = 2nn∈ N and 1 ≤ n ≤ 5}

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

Ans:- (iii) {5, 25, 125, 625}

It can be seen that 5 = 51, 25 = 52, 125 = 53, and 625 = 54.

∴ {5, 25, 125, 625} = {x: x = 5nn∈N and 1 ≤ n ≤ 4}

(iv) {2, 4, 6 …}

Ans:- (iv) {2, 4, 6 …}

It is a set of all even natural numbers.

∴ {2, 4, 6 …} = {x: x is an even natural number}

(v) {1, 4, 9 … 100}

Ans:- (v) {1, 4, 9 … 100}

It can be seen that 1 = 12, 4 = 22, 9 = 32 …100 = 102.

∴ {1, 4, 9… 100} = {x: x = n2n∈N and 1 ≤ n ≤ 10}

Q5:- List all the elements of the following sets:

(i) A = {xx is an odd natural number}

Ans:- (i) A = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}

(ii) B = {xx is an integer,}

Ans:- (ii) B = {x: x is an integer;}

It can be seen that  and 

∴ B 

(iii) C = {xx is an integer,}

Ans;- (iii) C = {x: x is an integer;}

It can be seen that

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

02 = 0 ≤ 4

12 = 1 ≤ 4

22 = 4 ≤ 4

32 = 9 > 4

∴C = {–2, –1, 0, 1, 2}

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

Ans:- (iv) D = (x: x is a letter in the word “LOYAL”) = {L, O, Y, A}

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

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

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

(vi) F = {xx is a consonant in the English alphabet which proceeds k}.

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

= {b, c, d, f, g, h, j}

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