Inter 1st Year Maths Sets Solutions Exercise 1a

Practicing the AP Board Solutions Class 11 Maths and Chapter 1 Inter 1st Year Maths Sets Solutions Exercise 1a Pdf Download will help students to clear their doubts quickly.

Intermediate 1st Year Maths Sets Solutions Exercise 1a

Sets Exercise 1a Solutions

Sets Class 11 Exercise 1a Solutions – Sets 1a Exercise Solutions

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.
(ii) The collection often most talented writers of India.
(iii) A team of eleven best cricket batsmen of the world.
(iv) The collection of all the boys in your class.
(v) The collection of all natural numbers less than 100.
(vi) A collection of novels written by the writer Munshi Prem Chand.
(vii) The collection of all even integers.
(viii) The collection of questions in this Chapter.
(ix) A collection of the most dangerous animals of the world.
Solution:
(i) The collection of all months of a year beginning with the letter J is a well-defined collection of objects, as one can identify a month that belongs to this collection.
Therefore, this collection is a set.

(ii) The collection of the ten most talented writers of India is not a well-defined collection, as the criteria to determine a batsman’s talent may vary from one person to another.
Therefore, this collection is not a set.

(iii) A team of eleven best cricket batsmen of the world is not a well-defined collection, as the criteria to determine a batsman’s talent may vary from one person to another.
Therefore, this collection is not a set.

(iv) The collection of all boys in your class is a well-defined collection, as you can identify a boy who belongs to this collection.
Therefore, this collection is a set.

(v) The collection of all natural numbers less than 100 is a well-defined collection, as one can find a number that belongs to this collection.
Therefore, this collection is a set.

(vi) A collection of novels written by the writer Muhshi Prem Chand is a well-defined collection, as one can find any book that belongs to this collection.
Therefore, this collection is a set.

(vii) The collection of all even integers is a well-defined collection, as one can find an integer that belongs to this collection.
Therefore, this collection is a set.

(viii) The collection of any questions in this chapter is a well-defined collection, as one can find a question that belongs to this chapter.
Therefore, this collection is a set.

(ix) A collection of the most dangerous animals of the world is not a well-defined collection, as the criteria to find the dangerousness of an animal can differ from one animal to another.
Therefore, this collection is not a set.

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) 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}
(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 = {x : x is an integer and -3 ≤ x < 7}
-2, -1, 0, 1, 2, 3, 4, 5, and 6 are the only elements of this set.
Hence, the given set can be written in roster form as A = {-2, -1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {-2, -1, 0, 1, 2, 3, 4, 5, 6}
1, 2, 3, 4, and 5 are the elements of this set.
Hence, the given set can be written in roster form as 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}
17, 26, 35, 44, 53, 62, 71, and 80 are the elements of this set.
Hence, the given set can be written in roster form as C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv) D = {x : x is a prime number which is divisor of 60}

Here 60 = 2 × 2 × 3 × 5
2, 3, and 5 are the only elements of this set.
Hence, the given set can be written in roster form as D = {2, 3, 5}

(v) E = The set of all letter words, out of which T, R, and O are repeated.
Hence, the given set can be written in roster form as E = {T, R, I, G, O, N, M, E, Y}

(vi) F = The set of all letters in the word BETTER.
BETTER is 6 6-letter word out of which E and T are repeated.
Hence, the given set can be written in roster form as 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) {3, 6, 9, 12}
The given set can be written in the set-builder form as {x: x = 3n, n ∈ N and 1 ≤ n ≤ 4}

(ii) {2, 4, 8, 10, 32}
We know that 2 = 2¹, 4 = 2², 8 = 2³, 16 = 2⁴ and 32 = 2⁵
Therefore, the given set {2, 4, 8, 16, 32} can be written in the set-builder form as {x : x = 2ⁿ, n ∈ N and 1 ≤ n ≤ 5}

(iii) {5, 25, 125, 625}
We know that 5 = 5¹, 25 = 5², 125 = 5³ and 625 = 5⁴
Therefore, the given set {5, 25, 125, 625} can be written in the Set-builder form as {x : x = 5ⁿ, n ∈ N and 1 ≤ n ≤ 4}

(iv) {2, 4, 6,…}
{2, 4, 6,…} is a set of all even natural numbers.
Therefore, the given set {2, 4, 6,…} can be written in the set-builder form as {x : x is an even natural number}

(v) {1, 4, 9,…,100}
We know that 1 = 1², 4 = 2², 9 = 3², ……, 100 = 10²
Therefore, the given set {1, 4, 9,…, 100} can be written in the set builder form as {x : x = n², n ∈ N and 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 = {x : x is an odd natural number}
So the elements are A = {1, 3, 5, 7, 9,…..}

(ii) B = {x : x is an integer, \(\frac{1}{2}<x<\frac{9}{2}\)}
We know that \(\frac {1}{2}\) = 0.5 and \(\frac {9}{2}\) = 4.5
So the elements are B = {0, 1, 2, 3, 4}

(iii) C = {x : x is an integer, x² ≤ 4}
We know that (-1)² = 1 ≤ 4; (-2)² = 4; (-3)² = 9 > 4
Here 0² = 0 ≤ 4, 1² = 1 ≤ 4, 2² = 4 ≤ 4, 3² = 9 > 4
So we get ⊂ {-2, -1, 0, 1, 2}

(iv) D = {x : x is a letter in the word “LOYAL”}
So the elements are D = {L, O, Y, A}

(v) E = {x: x is a month of a year not having 31 days}
So the elements are E = {February, April, June, September, November}

(vi) F = {x: x is a consonant in the English alphabet which precedes k}
So the elements are F = (b, c, d, f, g, h, j)

Question 6.
Match each of the sets 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 a natural number and a divisor of 6}
(iv) {1, 3, 5, 7, 9} (d) {x : x is a letter of the word MATHEMATICS}
Solution:
(i) Here, the elements of this set are natural numbers as well as divisors of 6.
Hence, (i) matches with (c).

(ii) 2 and 3 are prime numbers that are divisors of any 6.
Hence, (ii) matches with (a).

(iii) The elements are the letters of the word MATHEMATICS.
Hence, (iii) matches with (d).

(iv) The elements are odd natural numbers which are less than 10 above, (iv) matches with (b).