# 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 |

- 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}

- 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

- 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)

- 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, . . . }

- 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}

- 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}