Students can practice TS 10th Class Maths Solutions Chapter 2 Sets Ex 2.1 to get the best methods of solving problems.
TS 10th Class Maths Solutions Chapter 2 Sets Exercise 2.1
Question 1.
Which of the following are sets? Justify your answer.
(i) The collection of all the months of a year begining with the letter “J”.
Answer:
The months of a year which begin with the letter “J” are January, June and July.
The required set is {January, June, July}.
∴ The given statement is a well defined collection of objects. So, it is a set.
(ii) The collection of ten most talented writers of India.
Answer:
The given statement is not a set because the criterion for determining as most talented writers of India may vary from person to person. Thus, it is not a well defined collection.
(iii) A team of eleven best cricket batsmen of the world.
Answer:
The given statement is not a set because the criterion for determining eleven best cricket batsmen of the world may vary from person to person.
(iv) The collection of all boys in your class.
Answer:
The given statement is a set because given a student we can divide whether he/she belongs to the set or not.
(v) The collection of all even integers.
Answer:
The given statement is a set because given a number we can divide whether the number belongs to the given set or not.
Question 2.
If A = {0, 2, 4, 6}, B = {3, 5, 7} and C = {p, q, r}, then fill the appropriate symbol, ∈ or ∉ in the blanks.
(i) 0 ….. A
Answer:
0 ∈ A
(ii) 3 …… C
Answer:
3 ∉ C
(iii) 4 ….. B
Answer:
4 ∉ B
(iv) 8 ….. A
Answer:
8 ∉ A
(v) p …… C
Answer:
p ∈ C
(vi) 7 …… B
Answer:
7 ∈ B
Question 3.
Express the following statements using symbols.
(i) The element ‘x’ does not belong to ‘A’.
Answer:
x ∉ A
(ii) ‘d’ is an element of the set ‘B’.
Answer:
d ∈ B
(iii) ‘1’ belongs to the set of Natural numbers.
Answer:
1 ∈ N
(iv) ‘8’ does not belong to the set of prime numbers P.
Answer:
8 ∉ P
Question 4.
State whether the following statements are true or false. Justify your answer
(i) 5 ∉ set of prime numbers
Answer:
Not true (5 is a prime number)
(ii) S ∈ {5, 6, 7} implies 8 ∈ S.
Answer:
Not true (8 is not a member of S)
(iii) -5 ∉ W where ‘W’ is the set of whole numbers
Answer:
True (-5 is not a member of W)
(iv) \(\frac{8}{11}\) ∈ Z Where ‘Z’ is the set of integers.
Answer:
Not true (\(\frac{8}{11}\) is a rational number)
Question 5.
Write the following sets in roster form.
(i) B = {x : x is a natural number smaller than 6}
Answer:
B = {1, 2, 3, 4, 5}
(ii) C = {x : x is a two-digit natural number such that the sum of its digits is 8}.
Answer:
C = {17, 26, 35, 44, 53, 62, 71}
(iii) D = {x : x is a prime number which is a divisor of 60}.
Answer:
D = {3, 5}
(iv) E = {x : x is an alphabet in BETTER}.
Answer:
E = {B, E, T, R}
Question 6.
Write the following sets in the set-builder form.
(i) {3, 6, 9, 12}
Answer:
A = {x: x is multiple of 3 and less than 13}
(ii) {2, 4, 8, 16, 32}
Answer:
B = {x : x is in power of 2 and x is less than 6}
(iii) {5, 25, 125, 625}
Answer:
C = {x : x is in power of 5 and x is less than 5}
(iv) {1, 4, 9, 16, 25, 100}
Answer:
D = {x : x is in square of natural number and not greater than 10)
Question 7.
Write the following sets in roster form.
(i) A = {x : x is a natural number greater than 50 but smaller than 100}
Answer:
A = {51, 52, 53, 54….., 98, 99}
(ii) B = {x : x is an integer, x = 4}
Answer:
B = {+2, -2}
(iii) D = {x : x is a letter in the word “LOYAL”}
Answer:
D = {L, O, Y, A}
Question 8.
Match the roster form with set builder form.
Answer:
i) c
ii) a
iii) d
iv) b