# CHAPTER 1 : Sets

## Exercise 1.1

- Which of the following are sets ? Justify your answer.
- The collection of all the months of a year beginning with the letter J.
answer
- The collection of ten most talented writers of India.
answer
- A team of eleven best-cricket batsmen of the world.
answer
- The collection of all boys in your class.
answer
- The collection of all natural numbers less than 100.
answer
- A collection of novels written by the writer Munshi Prem Chand.
answer
- The collection of all even integers.
answer
- The collection of questions in this Chapter.
answer
- A collection of most dangerous animals of the world.
answer

- Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blank spaces:
- 5 …… A
- 8 …… A
- 0 …… A
- 4 …… A
- 2 …… A
- 10 …… A

answer
- Write the following sets in roster form:
- A = {x: x is an integer and –3 ≤ x < 7}
- B = {x: x is a natural number less than 6}
- C = {x: x is a two-digit natural number such that the sum of its digits is 8}
- D = {x: x is a prime number which is divisor of 60}
- E = The set of all letters in the word TRIGONOMETRY
- F = The set of all letters in the word BETTER

answer
- Write the following sets in the set-builder form:
- {3, 6, 9, 12}
- {2, 4, 8, 16, 32}
- {5, 25, 125, 625}
- {2, 4, 6, …}
- {1,4,9, … 100}

answer
- List all the elements of the following sets:
- A = {x : x is an odd natural number}
- B = {x : x is an integer, −1⁄2 < x < 9⁄2;}
- C = {x : x is an integer, x
^{2} ≤ 4}
- D = {x : x is a letter in the word “LOYAL”}
- E = {x : x is a month of a year not having 31 days}
- F = {x : x is a consonant in the English alphabet which precedes k}

answers
- Match each of the set on the left in the roster form with the same set on the right described in set-builder form:
- {1, 2, 3, 6}
(a) {x : x is a prime number and a divisor of 6}
- {2, 3}
(b) {x : x is an odd natural number less than 10}
- {M, A, T, H, E, I, C, S}
(c) {x : x is a natural number and divisor of 6}
- {1, 3, 5, 7, 9}
(d) {x : x is a letter of the word MATHEMATICS}

answer