Lecture 1 Sets Class 11 Maths

Lecture - 1 Chapter 1 Sets

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NCERT EXERCISE 1.1

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.

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

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

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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}

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, \frac{-1}{2}<x<\frac{9}{2} }
(iii) C = {x : x is an integer,x^2\le4}
(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 }.

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

NCERT EXERCISE 1.2
  1. Which of the following are examples of the null set
    • (i) Set of odd natural numbers divisible by 2
    • (ii) Set of even prime numbers
    • (iii) { x : x is a natural numbers, x < 5 and x > 7 }
  • (iv) { y : y is a point common to any two parallel lines}
  1. Which of the following sets are finite or infinite
    • (i) The set of months of a year
    • (ii) {1, 2, 3, . . .}
    • (iii) {1, 2, 3, . . .99, 100}
    • (iv) The set of positive integers greater than 100
    • (v) The set of prime numbers less than 99
  1. State whether each of the following set is finite or infinite:
    • (i) The set of lines which are parallel to the x-axis
    • (ii) The set of letters in the English alphabet
    • (iii) The set of numbers which are multiple of 5
    • (iv) The set of animals living on the earth
    • (v) The set of circles passing through the origin (0,0)
  1. In the following, state whether A = B or not:
  • (i) A = { a, b, c, d } B = { d, c, b, a }
  • (ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}
  • A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ≤ 10}
  • (iv) A = { x : x is a multiple of 10},  B = { 10, 15, 20, 25, 30, . . . }
  1. Are the following pair of sets equal? Give reasons.
    • (i) A = {2, 3}, B = {x : x is solution of }
    • (ii) A = { x : x is a letter in the word FOLLOW} B = { y : y is a letter in the word WOLF}
  1. From the sets given below, select equal sets:

A = { 2, 4, 8, 12},
B = { 1, 2, 3, 4},
C = { 4, 8, 12, 14},
D = { 3, 1, 4, 2}
E = {–1, 1},
F = { 0, a}
G = {1, –1}  
H = {0, 1}

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