Table of Contents
Exercise 2.1 Solutions – Class X Mathematics
These solutions are based on the Telangana State Class X Mathematics textbook, focusing on set theory concepts. Mathematical expressions are rendered using MathJax.
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”.
Conclusion: This is a set.
(ii) The collection of ten most talented writers of India.
Conclusion: This is not a set.
(iii) A team of eleven best cricket batsmen of the world.
Conclusion: This is not a set.
(iv) The collection of all boys in your class.
Conclusion: This is a set.
(v) The collection of all even integers.
Conclusion: This is a set.
2. If A = {0, 2, 4, 6}, B = {3, 5, 7} and C = {p, q, r}, then fill the appropriate symbol, \( \in \) or \( \notin \) in the blanks.
(i) 0 … A
Symbol = \(\in\)
(ii) 3 … C
Symbol = \(\notin\)
(iii) 4 … B
Symbol = \(\notin\)
(iv) p … C
Symbol = \(\in\)
(v) 7 … B
Symbol = \(\in\)
(vi) 7 … A
Symbol = \(\notin\)
3. Express the following statements using symbols.
(i) The element \( x \) does not belong to \( A \).
Symbol = \( x \notin A \)
(ii) \( d \) is an element of the set \( B \).
Symbol = \( d \in B \)
(iii) \( 1 \) belongs to the set of Natural numbers.
Symbol = \( 1 \in \mathbb{N} \)
(iv) \( 8 \) does not belong to the set of prime numbers \( P \).
Symbol = \( 8 \notin P \)
4. State whether the following statements are true or false. Justify your answer.
(i) 5 \( \in \) set of prime numbers
Conclusion: True
(ii) S = {5, 6, 7} implies 8 \( \in \) S.
Conclusion: False
(iii) -5 \( \in \) \( \mathbb{W} \) where \( \mathbb{W} \) is the set of whole numbers.
Conclusion: False
(iv) \( \frac{11}{2} \in \mathbb{Z} \) where \( \mathbb{Z} \) is the set of integers.
Conclusion: False
5. Write the following sets in roster form.
(i) B = {x : x is a natural number smaller than 6}
Roster form = {1, 2, 3, 4, 5}
(ii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}
Roster form = {17, 26, 35, 44, 53, 62, 71, 80}
(iii) D = {x : x is a prime number which is a divisor of 60}
Roster form = {2, 3, 5}
(iv) E = {x : x is an alphabet in BETTER}
Roster form = {B, E, T, R}
6. Write the following sets in the set-builder form.
(i) {3, 6, 9, 12}
Set-builder form = {x : x is a multiple of 3 and \( x \leq 12 \)}
(ii) {2, 4, 8, 16, 32}
Set-builder form = {x : x = 2^n, n is a natural number and \( x \leq 32 \)}
(iii) {5, 25, 125, 625}
Set-builder form = {x : x = 5^n, n is a natural number and \( x \leq 625 \)}
(iv) {1, 4, 9, 16, 25, …, 100}
Set-builder form = {x : x = n^2, n is a natural number and \( x \leq 100 \)}
7. Write the following sets in roster form.
(i) A = {x : x is a natural number greater than 50 but smaller than 100}
Roster form = {51, 52, 53, …, 99}
(ii) B = {x : x is an integer, \( x^2 < 4 \)}
Roster form = {-1, 0, 1}
(iii) D = {x : x is a letter in the word “LOYAL”}
Roster form = {L, O, Y, A}
8. Match the roster form with set-builder form.
(i) {1, 2, 3, 6}
Match = (a)
(ii) {2, 3}
Match = (c)
(iii) {m, a, t, h, e, i, c, s}
Match = (d)
(iv) {1, 3, 5, 7, 9}
Match = (b)
