NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.1
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(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.
(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) It is a set. The set of months in a year beginning with J is {January, June, July}.
(ii) The collection of ten most talented writers of India is not a set, because the term ‘most talented’ is not well defined.
(iii) A team of eleven best-cricket batsmen of the world is not a set, because the term ‘best-cricket batsman’ is not well defined.
(iv) The collection of all boys in your class is a set, because the boys in your class are welldefined.
(v) The collection of all natural numbers less than 100 is a set, because natural numbers less than 100 are {1, 2, 3,..., 99}.
(vi) The collection of novels written by the writer Munshi Prem Chand is a set, because this collection is well-defined.
(vii) The collection of all even integers is a set, because even integers are: {..., –4, –2, 0, 2, 4,..}.
(viii) The collection of questions in this chapter is a set, because the questions in this chapter are well-defined.
(ix) A collection of most dangerous animals of the world is not a set, because the term ‘most dangerous animal’ is not well defined.
2. Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ε 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 εA
(i) 5 εA
(ii) 8
A
A
(iii) 0 A
A
(iv) 4 εA
(v) 2 ε A
(vi) 10A
3. Write the following sets in roster form:
A3. 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 = {–2, 1, 0, 1, 2, 3, 4, 5, 6}
4. Write the following sets in the set-builder form:
Answer
(i) A = {–2, 1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {1, 2, 3, 4, 5}
(iii) C = {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = {2, 3, 5}
(v) E = {T, R, I, G, O, N, M, E, Y}
(vi) F = {B, E, T, R}.
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
5. List all the elements of the following sets:
Answer
(i) A = {x: x = 3n, n ε N and 1 ≤ n ≤ 4}
(ii) B = {x: x = 2n, n ε N and 1 ≤ n ≤ 5}
(iii) C = {x: x = 5n, n ε N and 1≤ n ≤ 4}
(iv) D = {x: x is an even natural number}
(v) E = {x: x = n2, n ε N and 1 ≤ n ≤ 10}
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, x2 ≤ 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
Answer
Answer
(i) A = {1, 3, 5,...}
(ii) B = {0, 1, 2, 3, 4}
(iii) C = {– 2, –1, 0, 1, 2}
(iv) D = {L, O, Y, A}
(v) E = {February, April, June, September, November}
(vi) 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 a natural number and divisor of 6} |
| (iv) {1, 3, 5, 7, 9} | (d) {x: x is a letter of the word |
Answer
| (i) {1, 2, 3, 6} | (c) {x: x is a natural number and divisor of 6} |
| (ii) {2, 3} | (a) {x: x is a prime number and 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} |