Sets Class 11 Exercise 1.1 Solutions

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. 

Solution: It is a set, as here defined elements are collected.

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

 Solution: It is not a set, as we cannot define who is most talented writer.

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

 Solution: It is not a set as definition of best batsman is not given.

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

 Solution: It is a set, since we can count the number of boys in your class.

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

 Solution: It is a set as we can write all the natural numbers less than 100.

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

Solution: It is a set because we know which book we have to pick.

(vii) The collection of all even integers.

Solution: It is a set as we know which element is inside the set (it is an infinite set but common property of element is well defined).

(viii) The collection of questions in this Chapter.

Solution: It is a set since we cannot doubt the elements of the set.

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

Solution: It is not a set, since we cannot say who is most dangerous animals.

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) ∈   (ii)∉   (iii)∉   (iv) ∈   (v)∈ (vi)∉ (elements ∈ Set)

3. Write the following sets in roster form:

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

Solution: {-3,-2,-1,0,1,2,4,5,6}

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

Solution: {1,2,3,4,5}

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

Solution: {17, 26, 35, 44, 53, 62, 71, 80}

(1+7=8, 2+6=8 and so on..)

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

Solution: {2,3,5}

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

Solution: {T,R,I,G,O,N,M,E,Y} (element can not repeat in a set )

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

Solution: {B,E,T,R} (element can not repeat in a set )

4. Write the following sets in the set-builder form :

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

Solution: {x : x = 3n, where n ∈ N and 1 ≤ x ≤ 4}

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

Solution: {x: x=2, where n∈N and 1 ≤ x ≤ 5}

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

Solution: {x: x=5, where n∈N and 1 ≤ x ≤ 5

(iv) {2, 4, 6, . . .}

Solution: {x: x=2n, where n∈N}

(v) {1,4,9, . . .,100}

Solution. {n: n∈N and n<=100}

5. List all the elements of the following sets :

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

Solution: A = {1, 3, 5, . . . }

(ii) B = {x : x is an integer, -½ < x < /}

Solution: B = {0, 1, 2, 3, 4 }

(iii) C = {x : x is an integer, x² ≤ 4}

Solution: C = { –2, –1, 0, 1, 2 }

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

Solution: D = { L, O, Y, A }

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

 Solution: E = { February, April, June, September, November }

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

Solution: F = {b, c, d, f, g, h, j }

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)