11th maths NCERT Sets Exercise 1.1 detailed solution with explanation

Question (1)

Which of the following are sets? Justify your answer.
(i) The collection of all months of a year beginning with the letter J.

Solution

Yes it is a set. as it is well defined collection of months.
(ii) The collection of ten most talented writers of India.

Solution

No it is not a set. There is no specific defination for talented writer. It changes person to person.
(iii) A team of eleven best cricket batsmen of the world.

Solution

No it is not a set. There is no specific defination for best batsmen. It changes person to person.
(iv) The collection of all boys in your class.

Solution

Yes it is a set. As it is collection of well defined persons.
(v) The collection of all natural numbers less than 100.

Solution

Yes it is a set as it well defined collection of numbers.
(vi)A collection of novels written by the writer Munshi Prem Chand.

Solution

Yes it is a set. It is the collection of books of one auther.
(vii) The collection of all even integers.

Solution

Yes it is a set as it well defined collection of numbers.
(viii) The collection of questions in this Chapter.

Solution

Yes it is a set. As it is collection of questions which is well defined.
(ix) A collection of most dangerous animals of the world.

Solution

No it is not a set. The most dangerous animals defination will change from person to person.

Question (2)

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

Solution

(i) 5 ∈ A
(ii) 8 ∉ A
(iii) 0 ∉ A
(iv) 4 ∈ A
(v) 2 ∈ A
(vi) 10 ∉ A

Question (3)

Write the following sets in roster form:
(i) A = {x: x is an integer and –3 < x < 7}.

Solution

A = { -2, -1, 0, 1, 2, 3, 4, 5, 6}
(ii) B = {x: x is a natural number less than 6}.

Solution

B = { 1, 2, 3, 4, 5}
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}

Solution

C = {17, 26, 35, 44, 53, 62, 71, 80}
(iv) D = {x: x is a prime number which is divisor of 60}.

Solution

D = { 2, 3, 5}
(v) E = The set of all letters in the word TRIGONOMETRY.

Solution

E = { T, R, I, G, O, N, M, E, Y}
(vi) F = The set of all letters in the word BETTER.

Solution

F = { B, E, T, R}

Question (4)

Write the following sets in the set-builder form:
(i) (3, 6, 9, 12)

Solution

A = First four natural multiples of 3.
A = { 3x / x ∈ N, x ≤ 4 }
(ii) {2, 4, 8, 16, 32}

Solution

B = { 2ⁿ , n ∈ N, n ≤ 5}
(iii) {5, 25, 125, 625}

Solution

C = { 5ⁿ , n ∈ N, n ≤ 4}
(iv) {2, 4, 6 …}

Solution

D the set of even natural numbers.
D = { 2n / n∈ N}
(v) {1, 4, 9 … 100}

Solution

E = The set of perfect square numbers less than 101.
E = { x² / x∈ N, x≤10}

Question (5)

List all the elements of the following sets:
(i) A = {x: x is an odd natural number}

Solution

A = { 1, 3, 5, 7, ........}
(ii) B = {x: x is an integer,-1/2 < x < 9/2}

Solution

B = { 0. 1. 2. 3, 4.}
(iii) C = {x: x is an integer,}

Solution

B = {.....-3, -2. -1. 0. 1. 2. 3. .........}
(iv) D = {x: x is a letter in the word “LOYAL”}

Solution

D = { L, O, Y, A}
(v) E = {x: x is a month of a year not having 31 days}
E = { February, April, june, September, November}

Solution

(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.

Solution

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: (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}

Solution

(i) ↔ c
(ii) ↔ a
(iii) ↔ d
(iv) ↔ b