AP Inter 1st Year Maths Exercise 1a Solutions

Referring to the AP Inter 1st Year Maths Study Material Chapter 1 Sets Exercise 1a Solutions makes it easier to understand complex problems.

AP Inter 1st Year Maths Sets Solutions Exercise 1a

Question 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.
Solution:
The collection of all the months of a year beginning with the letter J is a set because it is well defined.

ii) The collection of ten most talented writers of India.
Solution:
The collection of ten most talented writers of India is not a set because it is not well defined.

iii) A team of eleven best cricket batsmen of the world.
Solution:
A team of eleven best cricket batsmen of the world is not a set because it is not well defined.

iv) The collection of all boys in your class.
Solution:
The collection of all boys in my class is a set because it is well-defined.

v) The collection of all natural numbers less than 100.
Solution:
The collection of all natural numbers less than 100 is a set because it is well-defined.

vi) A collection of novels written by the writer Munshi Prem Chand.
Solution:
A collection of novels written by the writer Munshi Prem Chand is a set because it is well defined.

vii) The collection of all even integers.
Solution:
The collection of all even integers is a set because it is well defined.

viii) The collection of questions in this chapter.
Solution:
The collection of questions in this chapter is a set because it is well defined,

ix) A collection of most dangerous animals of the world.
Solution:
A collection of most dangerous animals of the world is not a set because it is not well defined.

Question 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
Solution:
i) ∈
ii) ∉
iii) ∉
iv) ∈
v) ∈
vi) ∉

Question 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}.
Solution:
i) A = {-3, -2,-1, 0, 1, 2, 3, 4, 5, 6}.
ii) B = {1, 2, 3, 4, 5}.
iii) C = {17, 26, 35, 44, 53, 62, 71, 80}.
iv) D = {2, 3, 5}.
v) E = {T, R, I, G, O, N, M, E, Y}.
vi) F = {B, E, T, R}.

Question 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}
Solution:
i) {x : x is a natural number multiple of 3 and x ≤ 15}.
ii) {x : x = 2n where n ∈ N & 1 ≤ n ≤ 5}.
iii) {x : x = 5n where ne N & 1 ≤ n ≤ 4}.
iv) { x : x is an even natural number}.
v) { x : x = n², 1 ≤ n ≤ 10}.

Question 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, x² ≤ 4).
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}.
Solution:
i) A = {1,3, 5, 7, ……….}.
ii) B = {0, 1,2, 3, 4}.
iii) C = {-2, -1, 0, 1, 2}.
iv) D = {L, O, Y, A},
v) E = {February, April, June, September, November},
vi) F = { b, c, d, f, g, h, j}

Question 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.

Answer: