“Twenty years from now you will be more disappointed by the things you didn’t do that the ones you did do. So throw off the bowlines. Catch the trade winds in your sails. Explore. Dream. Discover.” – Mark Twain

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

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}